Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2009-06

AUTHORS

M. S. Shahrokhi-Dehkordi, A. Taheri

ABSTRACT

Let be a bounded Lipschitz domain and consider the Dirichlet energy functionalover the space of measure preserving mapsIn this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler–Lagrange equations associated with over . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting previously unknown explicit formula. More... »

PAGES

191

References to SciGraph publications

  • 2005-06. Local Minimizers and Quasiconvexity – the Impact of Topology in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1976-12. Convexity conditions and existence theorems in nonlinear elasticity in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1999-12. On the partial regularity of energy-minimizing, area-preserving maps in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1976-05. Quasiconformal mappings and spaces of functions with generalized first derivatives in SIBERIAN MATHEMATICAL JOURNAL
  • 1983. Optimization—Theory and Applications, Problems with Ordinary Differential Equations in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00526-008-0202-5

    DOI

    http://dx.doi.org/10.1007/s00526-008-0202-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1043324250


    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 Sussex", 
              "id": "https://www.grid.ac/institutes/grid.12082.39", 
              "name": [
                "Department of Mathematics, University of Sussex, BN1 9RF, Falmer, Brighton, UK"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Shahrokhi-Dehkordi", 
            "givenName": "M. S.", 
            "id": "sg:person.010376531277.19", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010376531277.19"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Sussex", 
              "id": "https://www.grid.ac/institutes/grid.12082.39", 
              "name": [
                "Department of Mathematics, University of Sussex, BN1 9RF, Falmer, Brighton, UK"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Taheri", 
            "givenName": "A.", 
            "id": "sg:person.012013762300.12", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012013762300.12"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1080/03605309208820882", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015469420"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00967859", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021934980", 
              "https://doi.org/10.1007/bf00967859"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00967859", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021934980", 
              "https://doi.org/10.1007/bf00967859"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-005-0356-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030127409", 
              "https://doi.org/10.1007/s00205-005-0356-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-005-0356-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030127409", 
              "https://doi.org/10.1007/s00205-005-0356-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4613-8165-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030353457", 
              "https://doi.org/10.1007/978-1-4613-8165-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4613-8165-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030353457", 
              "https://doi.org/10.1007/978-1-4613-8165-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s005260050145", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041987999", 
              "https://doi.org/10.1007/s005260050145"
            ], 
            "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": "https://doi.org/10.12775/tmna.2009.013", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064665120"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2009-06", 
        "datePublishedReg": "2009-06-01", 
        "description": "Let be a bounded Lipschitz domain and consider the Dirichlet energy functionalover the space of measure preserving mapsIn this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler\u2013Lagrange equations associated with over . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting previously unknown explicit formula.", 
        "genre": "non_research_article", 
        "id": "sg:pub.10.1007/s00526-008-0202-5", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1043284", 
            "issn": [
              "0944-2669", 
              "1432-0835"
            ], 
            "name": "Calculus of Variations and Partial Differential Equations", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "35"
          }
        ], 
        "name": "Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps", 
        "pagination": "191", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "ce5edadc4fac56eeac2532b58dad19070d96bf23c3080648686b0da59a50d476"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00526-008-0202-5"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1043324250"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00526-008-0202-5", 
          "https://app.dimensions.ai/details/publication/pub.1043324250"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T14:31", 
        "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_13096_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs00526-008-0202-5"
      }
    ]
     

    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/s00526-008-0202-5'

    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/s00526-008-0202-5'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00526-008-0202-5'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00526-008-0202-5'


     

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

    94 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00526-008-0202-5 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ne07a6ea7dab042798ea4852dfdbc3d3b
    4 schema:citation sg:pub.10.1007/978-1-4613-8165-5
    5 sg:pub.10.1007/bf00279992
    6 sg:pub.10.1007/bf00967859
    7 sg:pub.10.1007/s00205-005-0356-7
    8 sg:pub.10.1007/s005260050145
    9 https://doi.org/10.1080/03605309208820882
    10 https://doi.org/10.12775/tmna.2009.013
    11 schema:datePublished 2009-06
    12 schema:datePublishedReg 2009-06-01
    13 schema:description Let be a bounded Lipschitz domain and consider the Dirichlet energy functionalover the space of measure preserving mapsIn this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler–Lagrange equations associated with over . The main result here is that in even dimensions the latter equations admit infinitely many solutions, modulo isometries, amongst such maps. We investigate various qualitative properties of these solutions in view of a remarkably interesting previously unknown explicit formula.
    14 schema:genre non_research_article
    15 schema:inLanguage en
    16 schema:isAccessibleForFree false
    17 schema:isPartOf N927f579fcfa4408fb8c9ebf99019c58f
    18 Nb93d6848846f4e9d8f69aa2b7bef1663
    19 sg:journal.1043284
    20 schema:name Generalised twists, stationary loops, and the Dirichlet energy over a space of measure preserving maps
    21 schema:pagination 191
    22 schema:productId Nbfab000862e84dd4bd0a1bec728f4fa7
    23 Nc39a78d33fd7410da6a7e432db6c5bf3
    24 Nfd8af8bfd07e44d8a2cc5ea878c69971
    25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043324250
    26 https://doi.org/10.1007/s00526-008-0202-5
    27 schema:sdDatePublished 2019-04-11T14:31
    28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    29 schema:sdPublisher Nb1f8748c4b1b4d498e2aba2d0293f94a
    30 schema:url http://link.springer.com/10.1007%2Fs00526-008-0202-5
    31 sgo:license sg:explorer/license/
    32 sgo:sdDataset articles
    33 rdf:type schema:ScholarlyArticle
    34 N008a51cee7db48e79f247b2dec43967d rdf:first sg:person.012013762300.12
    35 rdf:rest rdf:nil
    36 N927f579fcfa4408fb8c9ebf99019c58f schema:issueNumber 2
    37 rdf:type schema:PublicationIssue
    38 Nb1f8748c4b1b4d498e2aba2d0293f94a schema:name Springer Nature - SN SciGraph project
    39 rdf:type schema:Organization
    40 Nb93d6848846f4e9d8f69aa2b7bef1663 schema:volumeNumber 35
    41 rdf:type schema:PublicationVolume
    42 Nbfab000862e84dd4bd0a1bec728f4fa7 schema:name readcube_id
    43 schema:value ce5edadc4fac56eeac2532b58dad19070d96bf23c3080648686b0da59a50d476
    44 rdf:type schema:PropertyValue
    45 Nc39a78d33fd7410da6a7e432db6c5bf3 schema:name doi
    46 schema:value 10.1007/s00526-008-0202-5
    47 rdf:type schema:PropertyValue
    48 Ne07a6ea7dab042798ea4852dfdbc3d3b rdf:first sg:person.010376531277.19
    49 rdf:rest N008a51cee7db48e79f247b2dec43967d
    50 Nfd8af8bfd07e44d8a2cc5ea878c69971 schema:name dimensions_id
    51 schema:value pub.1043324250
    52 rdf:type schema:PropertyValue
    53 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    54 schema:name Mathematical Sciences
    55 rdf:type schema:DefinedTerm
    56 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Pure Mathematics
    58 rdf:type schema:DefinedTerm
    59 sg:journal.1043284 schema:issn 0944-2669
    60 1432-0835
    61 schema:name Calculus of Variations and Partial Differential Equations
    62 rdf:type schema:Periodical
    63 sg:person.010376531277.19 schema:affiliation https://www.grid.ac/institutes/grid.12082.39
    64 schema:familyName Shahrokhi-Dehkordi
    65 schema:givenName M. S.
    66 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010376531277.19
    67 rdf:type schema:Person
    68 sg:person.012013762300.12 schema:affiliation https://www.grid.ac/institutes/grid.12082.39
    69 schema:familyName Taheri
    70 schema:givenName A.
    71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012013762300.12
    72 rdf:type schema:Person
    73 sg:pub.10.1007/978-1-4613-8165-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030353457
    74 https://doi.org/10.1007/978-1-4613-8165-5
    75 rdf:type schema:CreativeWork
    76 sg:pub.10.1007/bf00279992 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048187466
    77 https://doi.org/10.1007/bf00279992
    78 rdf:type schema:CreativeWork
    79 sg:pub.10.1007/bf00967859 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021934980
    80 https://doi.org/10.1007/bf00967859
    81 rdf:type schema:CreativeWork
    82 sg:pub.10.1007/s00205-005-0356-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030127409
    83 https://doi.org/10.1007/s00205-005-0356-7
    84 rdf:type schema:CreativeWork
    85 sg:pub.10.1007/s005260050145 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041987999
    86 https://doi.org/10.1007/s005260050145
    87 rdf:type schema:CreativeWork
    88 https://doi.org/10.1080/03605309208820882 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015469420
    89 rdf:type schema:CreativeWork
    90 https://doi.org/10.12775/tmna.2009.013 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064665120
    91 rdf:type schema:CreativeWork
    92 https://www.grid.ac/institutes/grid.12082.39 schema:alternateName University of Sussex
    93 schema:name Department of Mathematics, University of Sussex, BN1 9RF, Falmer, Brighton, UK
    94 rdf:type schema:Organization
     




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


    ...