Local Minimizers and Quasiconvexity – the Impact of Topology View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-06

AUTHORS

Ali Taheri

ABSTRACT

The aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals : from a purely topological point of view. The basic assumptions on are sequential lower semicontinuity with respect to W1,p-weak convergence and W1,p-weak coercivity, and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds and . In the first part of the paper, we focus on the case where is non-contractible and proceed by establishing a link between the latter problem and the question of enumeration of homotopy classes of continuous maps from various skeleta of into . As this in turn can be tackled by the so-called obstruction method, it is evident that our results in this direction are of a cohomological nature. The second part is devoted to the case where =ℝN and is a bounded smooth domain. In particular we consider integrals where the above assumptions on can be verified when the integrand F is quasiconvex and pointwise p-coercive with respect to the gradient argument. We introduce and exploit the notion of a topologically non-trivial domain and under this establish the first existence and multiplicity result for strong local minimizers of that in turn settles a longstanding open problem in the multi-dimensional calculus of variations as described in [6]. More... »

PAGES

363-414

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-005-0356-7

DOI

http://dx.doi.org/10.1007/s00205-005-0356-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1030127409


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Oxford", 
          "id": "https://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Mathematical Institute, University of Oxford, 24\u201329 St Giles\u2019, OX1 3LB, Oxford, England, U.K"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Taheri", 
        "givenName": "Ali", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1112/blms/15.5.401", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000304326"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02921588", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001387344", 
          "https://doi.org/10.1007/bf02921588"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00282200", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002439485", 
          "https://doi.org/10.1007/bf00282200"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00282200", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002439485", 
          "https://doi.org/10.1007/bf00282200"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00275731", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003130524", 
          "https://doi.org/10.1007/bf00275731"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00275731", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003130524", 
          "https://doi.org/10.1007/bf00275731"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1965-0188838-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003534599"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-1236(81)90085-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004222945"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02391853", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004460810", 
          "https://doi.org/10.1007/bf02391853"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9904-1964-11062-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005108778"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00205-003-0275-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005722420", 
          "https://doi.org/10.1007/s00205-003-0275-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-9383(63)90013-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006859835"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-1236(88)90065-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007147514"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/0-387-21791-6_1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008495768", 
          "https://doi.org/10.1007/0-387-21791-6_1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/s0024610703004253", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009379456"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s005260050092", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013479264", 
          "https://doi.org/10.1007/s005260050092"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1956-0079265-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015316988"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-9383(66)90013-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017872395"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00386070", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019937650", 
          "https://doi.org/10.1007/bf00386070"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00386070", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019937650", 
          "https://doi.org/10.1007/bf00386070"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-1959-0112149-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020698832"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-03-06852-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022622687"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-1236(72)90039-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022642239"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/blms/15.4.360", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023016186"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02921593", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025609864", 
          "https://doi.org/10.1007/bf02921593"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02392271", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026391347", 
          "https://doi.org/10.1007/bf02392271"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00375279", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028008068", 
          "https://doi.org/10.1007/bf00375279"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-9383(66)90002-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028563661"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s005260050137", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035924343", 
          "https://doi.org/10.1007/s005260050137"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1981-0626490-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040609318"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01283844", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041921683", 
          "https://doi.org/10.1007/bf01283844"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160250505", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043984713"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160250505", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043984713"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0040-9383(76)90042-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044890697"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0362-546x(94)90190-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045309228"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02103722", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047143500", 
          "https://doi.org/10.1007/bf02103722"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02103722", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047143500", 
          "https://doi.org/10.1007/bf02103722"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00279992", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048187466", 
          "https://doi.org/10.1007/bf00279992"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00279992", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048187466", 
          "https://doi.org/10.1007/bf00279992"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00279992", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048187466", 
          "https://doi.org/10.1007/bf00279992"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s005260100122", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048815437", 
          "https://doi.org/10.1007/s005260100122"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-6318-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048896065", 
          "https://doi.org/10.1007/978-1-4612-6318-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-6318-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048896065", 
          "https://doi.org/10.1007/978-1-4612-6318-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00281557", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048959497", 
          "https://doi.org/10.1007/bf00281557"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jfan.2000.3736", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050307567"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01209163", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051542939", 
          "https://doi.org/10.1007/bf01209163"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02392449", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051966041", 
          "https://doi.org/10.1007/bf02392449"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-51440-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052008351", 
          "https://doi.org/10.1007/978-3-642-51440-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-51440-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052008351", 
          "https://doi.org/10.1007/978-3-642-51440-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500000822", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054892323"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500000822", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054892323"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500000822", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054892323"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500015006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054893205"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500018199", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054893503"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s030821050002014x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054893697"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500025026", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054894185"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500029929", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054894674"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500030353", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054894717"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/qmath/25.1.313", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059987690"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036141094263767", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062876260"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/s0012-7094-37-00306-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064415842"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/s0012-7094-39-00554-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064416023"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.12775/tmna.1999.009", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064664827"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969085", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069674483"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969401", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069674784"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969510", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069674886"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969745", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069675110"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969748", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069675113"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1971131", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069676430"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2373248", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069899828"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4153/cjm-1981-059-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072266777"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.2001.v8.n3.a8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072462092"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0294-1449(16)30193-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1083544864"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/jdg/1214434347", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084459243"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/jdg/1214437663", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084459439"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/jdg/1214440023", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084459551"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/cbo9780511623912", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098664015"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2005-06", 
    "datePublishedReg": "2005-06-01", 
    "description": "The aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals : from a purely topological point of view. The basic assumptions on are sequential lower semicontinuity with respect to W1,p-weak convergence and W1,p-weak coercivity, and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds and . In the first part of the paper, we focus on the case where is non-contractible and proceed by establishing a link between the latter problem and the question of enumeration of homotopy classes of continuous maps from various skeleta of into . As this in turn can be tackled by the so-called obstruction method, it is evident that our results in this direction are of a cohomological nature. The second part is devoted to the case where =\u211dN and is a bounded smooth domain. In particular we consider integrals  where the above assumptions on can be verified when the integrand F is quasiconvex and pointwise p-coercive with respect to the gradient argument. We introduce and exploit the notion of a topologically non-trivial domain and under this establish the first existence and multiplicity result for strong local minimizers of that in turn settles a longstanding open problem in the multi-dimensional calculus of variations as described in [6].", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00205-005-0356-7", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1047617", 
        "issn": [
          "0003-9527", 
          "1432-0673"
        ], 
        "name": "Archive for Rational Mechanics and Analysis", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "176"
      }
    ], 
    "name": "Local Minimizers and Quasiconvexity \u2013 the Impact of Topology", 
    "pagination": "363-414", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "8f861e19fe6f644a3c2ac5e9150ffecb7e3e0b6b8478625003d5e46759999282"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00205-005-0356-7"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1030127409"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00205-005-0356-7", 
      "https://app.dimensions.ai/details/publication/pub.1030127409"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:33", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13104_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs00205-005-0356-7"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00205-005-0356-7'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00205-005-0356-7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00205-005-0356-7'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00205-005-0356-7'


 

This table displays all metadata directly associated to this object as RDF triples.

279 TRIPLES      21 PREDICATES      93 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00205-005-0356-7 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N8bdd4b58b85c4416bf25fe39a12ea3c2
4 schema:citation sg:pub.10.1007/0-387-21791-6_1
5 sg:pub.10.1007/978-1-4612-6318-0
6 sg:pub.10.1007/978-3-642-51440-1
7 sg:pub.10.1007/bf00275731
8 sg:pub.10.1007/bf00279992
9 sg:pub.10.1007/bf00281557
10 sg:pub.10.1007/bf00282200
11 sg:pub.10.1007/bf00375279
12 sg:pub.10.1007/bf00386070
13 sg:pub.10.1007/bf01209163
14 sg:pub.10.1007/bf01283844
15 sg:pub.10.1007/bf02103722
16 sg:pub.10.1007/bf02391853
17 sg:pub.10.1007/bf02392271
18 sg:pub.10.1007/bf02392449
19 sg:pub.10.1007/bf02921588
20 sg:pub.10.1007/bf02921593
21 sg:pub.10.1007/s00205-003-0275-4
22 sg:pub.10.1007/s005260050092
23 sg:pub.10.1007/s005260050137
24 sg:pub.10.1007/s005260100122
25 https://doi.org/10.1002/cpa.3160250505
26 https://doi.org/10.1006/jfan.2000.3736
27 https://doi.org/10.1016/0022-1236(72)90039-0
28 https://doi.org/10.1016/0022-1236(81)90085-9
29 https://doi.org/10.1016/0022-1236(88)90065-1
30 https://doi.org/10.1016/0040-9383(63)90013-2
31 https://doi.org/10.1016/0040-9383(66)90002-4
32 https://doi.org/10.1016/0040-9383(66)90013-9
33 https://doi.org/10.1016/0040-9383(76)90042-2
34 https://doi.org/10.1016/0362-546x(94)90190-2
35 https://doi.org/10.1016/s0294-1449(16)30193-7
36 https://doi.org/10.1017/cbo9780511623912
37 https://doi.org/10.1017/s0308210500000822
38 https://doi.org/10.1017/s0308210500015006
39 https://doi.org/10.1017/s0308210500018199
40 https://doi.org/10.1017/s030821050002014x
41 https://doi.org/10.1017/s0308210500025026
42 https://doi.org/10.1017/s0308210500029929
43 https://doi.org/10.1017/s0308210500030353
44 https://doi.org/10.1090/s0002-9904-1964-11062-4
45 https://doi.org/10.1090/s0002-9939-03-06852-7
46 https://doi.org/10.1090/s0002-9939-1959-0112149-8
47 https://doi.org/10.1090/s0002-9947-1956-0079265-2
48 https://doi.org/10.1090/s0002-9947-1965-0188838-3
49 https://doi.org/10.1090/s0002-9947-1981-0626490-x
50 https://doi.org/10.1093/qmath/25.1.313
51 https://doi.org/10.1112/blms/15.4.360
52 https://doi.org/10.1112/blms/15.5.401
53 https://doi.org/10.1112/s0024610703004253
54 https://doi.org/10.1137/s0036141094263767
55 https://doi.org/10.1215/s0012-7094-37-00306-5
56 https://doi.org/10.1215/s0012-7094-39-00554-5
57 https://doi.org/10.12775/tmna.1999.009
58 https://doi.org/10.2307/1969085
59 https://doi.org/10.2307/1969401
60 https://doi.org/10.2307/1969510
61 https://doi.org/10.2307/1969745
62 https://doi.org/10.2307/1969748
63 https://doi.org/10.2307/1971131
64 https://doi.org/10.2307/2373248
65 https://doi.org/10.4153/cjm-1981-059-7
66 https://doi.org/10.4310/jdg/1214434347
67 https://doi.org/10.4310/jdg/1214437663
68 https://doi.org/10.4310/jdg/1214440023
69 https://doi.org/10.4310/mrl.2001.v8.n3.a8
70 schema:datePublished 2005-06
71 schema:datePublishedReg 2005-06-01
72 schema:description The aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals : from a purely topological point of view. The basic assumptions on are sequential lower semicontinuity with respect to W1,p-weak convergence and W1,p-weak coercivity, and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds and . In the first part of the paper, we focus on the case where is non-contractible and proceed by establishing a link between the latter problem and the question of enumeration of homotopy classes of continuous maps from various skeleta of into . As this in turn can be tackled by the so-called obstruction method, it is evident that our results in this direction are of a cohomological nature. The second part is devoted to the case where =ℝN and is a bounded smooth domain. In particular we consider integrals where the above assumptions on can be verified when the integrand F is quasiconvex and pointwise p-coercive with respect to the gradient argument. We introduce and exploit the notion of a topologically non-trivial domain and under this establish the first existence and multiplicity result for strong local minimizers of that in turn settles a longstanding open problem in the multi-dimensional calculus of variations as described in [6].
73 schema:genre research_article
74 schema:inLanguage en
75 schema:isAccessibleForFree false
76 schema:isPartOf N02b4ec84759d49afa574909d90eabb8f
77 N55eb3036eefa419584e66a98413586c3
78 sg:journal.1047617
79 schema:name Local Minimizers and Quasiconvexity – the Impact of Topology
80 schema:pagination 363-414
81 schema:productId N06b97353707342a0a95b7a103e292b0e
82 Nab8bc4a29fc842388b2bdcbc0dfbac83
83 Ne61414ee5e28494a81d432af05fc499e
84 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030127409
85 https://doi.org/10.1007/s00205-005-0356-7
86 schema:sdDatePublished 2019-04-11T14:33
87 schema:sdLicense https://scigraph.springernature.com/explorer/license/
88 schema:sdPublisher N047e92bad1bc4c4796672682dc0a71dd
89 schema:url http://link.springer.com/10.1007%2Fs00205-005-0356-7
90 sgo:license sg:explorer/license/
91 sgo:sdDataset articles
92 rdf:type schema:ScholarlyArticle
93 N02b4ec84759d49afa574909d90eabb8f schema:volumeNumber 176
94 rdf:type schema:PublicationVolume
95 N047e92bad1bc4c4796672682dc0a71dd schema:name Springer Nature - SN SciGraph project
96 rdf:type schema:Organization
97 N06b97353707342a0a95b7a103e292b0e schema:name dimensions_id
98 schema:value pub.1030127409
99 rdf:type schema:PropertyValue
100 N2146595ed39747e0a56ae0fb1582bafd schema:affiliation https://www.grid.ac/institutes/grid.4991.5
101 schema:familyName Taheri
102 schema:givenName Ali
103 rdf:type schema:Person
104 N55eb3036eefa419584e66a98413586c3 schema:issueNumber 3
105 rdf:type schema:PublicationIssue
106 N8bdd4b58b85c4416bf25fe39a12ea3c2 rdf:first N2146595ed39747e0a56ae0fb1582bafd
107 rdf:rest rdf:nil
108 Nab8bc4a29fc842388b2bdcbc0dfbac83 schema:name doi
109 schema:value 10.1007/s00205-005-0356-7
110 rdf:type schema:PropertyValue
111 Ne61414ee5e28494a81d432af05fc499e schema:name readcube_id
112 schema:value 8f861e19fe6f644a3c2ac5e9150ffecb7e3e0b6b8478625003d5e46759999282
113 rdf:type schema:PropertyValue
114 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
115 schema:name Mathematical Sciences
116 rdf:type schema:DefinedTerm
117 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
118 schema:name Pure Mathematics
119 rdf:type schema:DefinedTerm
120 sg:journal.1047617 schema:issn 0003-9527
121 1432-0673
122 schema:name Archive for Rational Mechanics and Analysis
123 rdf:type schema:Periodical
124 sg:pub.10.1007/0-387-21791-6_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008495768
125 https://doi.org/10.1007/0-387-21791-6_1
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/978-1-4612-6318-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048896065
128 https://doi.org/10.1007/978-1-4612-6318-0
129 rdf:type schema:CreativeWork
130 sg:pub.10.1007/978-3-642-51440-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052008351
131 https://doi.org/10.1007/978-3-642-51440-1
132 rdf:type schema:CreativeWork
133 sg:pub.10.1007/bf00275731 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003130524
134 https://doi.org/10.1007/bf00275731
135 rdf:type schema:CreativeWork
136 sg:pub.10.1007/bf00279992 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048187466
137 https://doi.org/10.1007/bf00279992
138 rdf:type schema:CreativeWork
139 sg:pub.10.1007/bf00281557 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048959497
140 https://doi.org/10.1007/bf00281557
141 rdf:type schema:CreativeWork
142 sg:pub.10.1007/bf00282200 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002439485
143 https://doi.org/10.1007/bf00282200
144 rdf:type schema:CreativeWork
145 sg:pub.10.1007/bf00375279 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028008068
146 https://doi.org/10.1007/bf00375279
147 rdf:type schema:CreativeWork
148 sg:pub.10.1007/bf00386070 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019937650
149 https://doi.org/10.1007/bf00386070
150 rdf:type schema:CreativeWork
151 sg:pub.10.1007/bf01209163 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051542939
152 https://doi.org/10.1007/bf01209163
153 rdf:type schema:CreativeWork
154 sg:pub.10.1007/bf01283844 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041921683
155 https://doi.org/10.1007/bf01283844
156 rdf:type schema:CreativeWork
157 sg:pub.10.1007/bf02103722 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047143500
158 https://doi.org/10.1007/bf02103722
159 rdf:type schema:CreativeWork
160 sg:pub.10.1007/bf02391853 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004460810
161 https://doi.org/10.1007/bf02391853
162 rdf:type schema:CreativeWork
163 sg:pub.10.1007/bf02392271 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026391347
164 https://doi.org/10.1007/bf02392271
165 rdf:type schema:CreativeWork
166 sg:pub.10.1007/bf02392449 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051966041
167 https://doi.org/10.1007/bf02392449
168 rdf:type schema:CreativeWork
169 sg:pub.10.1007/bf02921588 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001387344
170 https://doi.org/10.1007/bf02921588
171 rdf:type schema:CreativeWork
172 sg:pub.10.1007/bf02921593 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025609864
173 https://doi.org/10.1007/bf02921593
174 rdf:type schema:CreativeWork
175 sg:pub.10.1007/s00205-003-0275-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005722420
176 https://doi.org/10.1007/s00205-003-0275-4
177 rdf:type schema:CreativeWork
178 sg:pub.10.1007/s005260050092 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013479264
179 https://doi.org/10.1007/s005260050092
180 rdf:type schema:CreativeWork
181 sg:pub.10.1007/s005260050137 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035924343
182 https://doi.org/10.1007/s005260050137
183 rdf:type schema:CreativeWork
184 sg:pub.10.1007/s005260100122 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048815437
185 https://doi.org/10.1007/s005260100122
186 rdf:type schema:CreativeWork
187 https://doi.org/10.1002/cpa.3160250505 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043984713
188 rdf:type schema:CreativeWork
189 https://doi.org/10.1006/jfan.2000.3736 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050307567
190 rdf:type schema:CreativeWork
191 https://doi.org/10.1016/0022-1236(72)90039-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022642239
192 rdf:type schema:CreativeWork
193 https://doi.org/10.1016/0022-1236(81)90085-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004222945
194 rdf:type schema:CreativeWork
195 https://doi.org/10.1016/0022-1236(88)90065-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007147514
196 rdf:type schema:CreativeWork
197 https://doi.org/10.1016/0040-9383(63)90013-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006859835
198 rdf:type schema:CreativeWork
199 https://doi.org/10.1016/0040-9383(66)90002-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028563661
200 rdf:type schema:CreativeWork
201 https://doi.org/10.1016/0040-9383(66)90013-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017872395
202 rdf:type schema:CreativeWork
203 https://doi.org/10.1016/0040-9383(76)90042-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044890697
204 rdf:type schema:CreativeWork
205 https://doi.org/10.1016/0362-546x(94)90190-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045309228
206 rdf:type schema:CreativeWork
207 https://doi.org/10.1016/s0294-1449(16)30193-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083544864
208 rdf:type schema:CreativeWork
209 https://doi.org/10.1017/cbo9780511623912 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098664015
210 rdf:type schema:CreativeWork
211 https://doi.org/10.1017/s0308210500000822 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054892323
212 rdf:type schema:CreativeWork
213 https://doi.org/10.1017/s0308210500015006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054893205
214 rdf:type schema:CreativeWork
215 https://doi.org/10.1017/s0308210500018199 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054893503
216 rdf:type schema:CreativeWork
217 https://doi.org/10.1017/s030821050002014x schema:sameAs https://app.dimensions.ai/details/publication/pub.1054893697
218 rdf:type schema:CreativeWork
219 https://doi.org/10.1017/s0308210500025026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054894185
220 rdf:type schema:CreativeWork
221 https://doi.org/10.1017/s0308210500029929 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054894674
222 rdf:type schema:CreativeWork
223 https://doi.org/10.1017/s0308210500030353 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054894717
224 rdf:type schema:CreativeWork
225 https://doi.org/10.1090/s0002-9904-1964-11062-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005108778
226 rdf:type schema:CreativeWork
227 https://doi.org/10.1090/s0002-9939-03-06852-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022622687
228 rdf:type schema:CreativeWork
229 https://doi.org/10.1090/s0002-9939-1959-0112149-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020698832
230 rdf:type schema:CreativeWork
231 https://doi.org/10.1090/s0002-9947-1956-0079265-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015316988
232 rdf:type schema:CreativeWork
233 https://doi.org/10.1090/s0002-9947-1965-0188838-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003534599
234 rdf:type schema:CreativeWork
235 https://doi.org/10.1090/s0002-9947-1981-0626490-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1040609318
236 rdf:type schema:CreativeWork
237 https://doi.org/10.1093/qmath/25.1.313 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059987690
238 rdf:type schema:CreativeWork
239 https://doi.org/10.1112/blms/15.4.360 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023016186
240 rdf:type schema:CreativeWork
241 https://doi.org/10.1112/blms/15.5.401 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000304326
242 rdf:type schema:CreativeWork
243 https://doi.org/10.1112/s0024610703004253 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009379456
244 rdf:type schema:CreativeWork
245 https://doi.org/10.1137/s0036141094263767 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062876260
246 rdf:type schema:CreativeWork
247 https://doi.org/10.1215/s0012-7094-37-00306-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064415842
248 rdf:type schema:CreativeWork
249 https://doi.org/10.1215/s0012-7094-39-00554-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064416023
250 rdf:type schema:CreativeWork
251 https://doi.org/10.12775/tmna.1999.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064664827
252 rdf:type schema:CreativeWork
253 https://doi.org/10.2307/1969085 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674483
254 rdf:type schema:CreativeWork
255 https://doi.org/10.2307/1969401 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674784
256 rdf:type schema:CreativeWork
257 https://doi.org/10.2307/1969510 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674886
258 rdf:type schema:CreativeWork
259 https://doi.org/10.2307/1969745 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069675110
260 rdf:type schema:CreativeWork
261 https://doi.org/10.2307/1969748 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069675113
262 rdf:type schema:CreativeWork
263 https://doi.org/10.2307/1971131 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069676430
264 rdf:type schema:CreativeWork
265 https://doi.org/10.2307/2373248 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069899828
266 rdf:type schema:CreativeWork
267 https://doi.org/10.4153/cjm-1981-059-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072266777
268 rdf:type schema:CreativeWork
269 https://doi.org/10.4310/jdg/1214434347 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084459243
270 rdf:type schema:CreativeWork
271 https://doi.org/10.4310/jdg/1214437663 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084459439
272 rdf:type schema:CreativeWork
273 https://doi.org/10.4310/jdg/1214440023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084459551
274 rdf:type schema:CreativeWork
275 https://doi.org/10.4310/mrl.2001.v8.n3.a8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072462092
276 rdf:type schema:CreativeWork
277 https://www.grid.ac/institutes/grid.4991.5 schema:alternateName University of Oxford
278 schema:name Mathematical Institute, University of Oxford, 24–29 St Giles’, OX1 3LB, Oxford, England, U.K
279 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...