Gamma-convergence of nonlocal perimeter functionals View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-03

AUTHORS

Luigi Ambrosio, Guido De Philippis, Luca Martinazzi

ABSTRACT

Given open, connected and with Lipschitz boundary, and , we consider the functionalwhere is an arbitrary measurable set. We prove that the functionals are equi-coercive in as and thatwhere P(E, Ω) denotes the perimeter of E in Ω in the sense of De Giorgi. We also prove that as limit points of local minimizers of are local minimizers of P(·, Ω). More... »

PAGES

377-403

References to SciGraph publications

  • 1991-06. Generalized coarea formula and fractal sets in JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
  • 2011-05. Uniform estimates and limiting arguments for nonlocal minimal surfaces in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1984. Minimal Surfaces and Functions of Bounded Variation in NONE
  • Journal

    TITLE

    manuscripta mathematica

    ISSUE

    3-4

    VOLUME

    134

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00229-010-0399-4

    DOI

    http://dx.doi.org/10.1007/s00229-010-0399-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1051699194


    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/2008/1608", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Sociology", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/16", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Studies in Human Society", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Scuola Normale Superiore di Pisa", 
              "id": "https://www.grid.ac/institutes/grid.6093.c", 
              "name": [
                "Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ambrosio", 
            "givenName": "Luigi", 
            "id": "sg:person.012621721115.68", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Scuola Normale Superiore di Pisa", 
              "id": "https://www.grid.ac/institutes/grid.6093.c", 
              "name": [
                "Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Philippis", 
            "givenName": "Guido De", 
            "id": "sg:person.011510274777.31", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011510274777.31"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "name": [
                "Centro De Giorgi, Pisa, Italy"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Martinazzi", 
            "givenName": "Luca", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-1-4684-9486-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006563782", 
              "https://doi.org/10.1007/978-1-4684-9486-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4684-9486-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006563782", 
              "https://doi.org/10.1007/978-1-4684-9486-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-1947-0020618-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008281265"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.20331", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011323931"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1002/cpa.20331", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011323931"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1013789647", 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1013789647", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-010-0359-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017063594", 
              "https://doi.org/10.1007/s00526-010-0359-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03167679", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045616123", 
              "https://doi.org/10.1007/bf03167679"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf03167679", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1045616123", 
              "https://doi.org/10.1007/bf03167679"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-1236(03)00002-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048812310"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0022-1236(03)00002-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048812310"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/0523060", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062848473"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/jems/108", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072317680"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2011-03", 
        "datePublishedReg": "2011-03-01", 
        "description": "Given open, connected and with Lipschitz boundary, and , we consider the functionalwhere is an arbitrary measurable set. We prove that the functionals are equi-coercive in as and thatwhere P(E, \u03a9) denotes the perimeter of E in \u03a9 in the sense of De Giorgi. We also prove that as limit points of local minimizers of are local minimizers of P(\u00b7, \u03a9).", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00229-010-0399-4", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136220", 
            "issn": [
              "0025-2611", 
              "1432-1785"
            ], 
            "name": "manuscripta mathematica", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3-4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "134"
          }
        ], 
        "name": "Gamma-convergence of nonlocal perimeter functionals", 
        "pagination": "377-403", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "f644cae1779c97fe82945c751b82b52522696c577da70cdc307d06a39e6f9a91"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00229-010-0399-4"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1051699194"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00229-010-0399-4", 
          "https://app.dimensions.ai/details/publication/pub.1051699194"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T16:43", 
        "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/v90/0000000001_0000000264/records_8669_00000516.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs00229-010-0399-4"
      }
    ]
     

    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/s00229-010-0399-4'

    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/s00229-010-0399-4'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00229-010-0399-4'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00229-010-0399-4'


     

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

    105 TRIPLES      21 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00229-010-0399-4 schema:about anzsrc-for:16
    2 anzsrc-for:1608
    3 schema:author N7342a0f90a434b6eb61c9424fdce36d1
    4 schema:citation sg:pub.10.1007/978-1-4684-9486-0
    5 sg:pub.10.1007/bf03167679
    6 sg:pub.10.1007/s00526-010-0359-6
    7 https://app.dimensions.ai/details/publication/pub.1013789647
    8 https://doi.org/10.1002/cpa.20331
    9 https://doi.org/10.1016/s0022-1236(03)00002-8
    10 https://doi.org/10.1090/s0002-9947-1947-0020618-0
    11 https://doi.org/10.1137/0523060
    12 https://doi.org/10.4171/jems/108
    13 schema:datePublished 2011-03
    14 schema:datePublishedReg 2011-03-01
    15 schema:description Given open, connected and with Lipschitz boundary, and , we consider the functionalwhere is an arbitrary measurable set. We prove that the functionals are equi-coercive in as and thatwhere P(E, Ω) denotes the perimeter of E in Ω in the sense of De Giorgi. We also prove that as limit points of local minimizers of are local minimizers of P(·, Ω).
    16 schema:genre research_article
    17 schema:inLanguage en
    18 schema:isAccessibleForFree true
    19 schema:isPartOf N4cfed65af2714f5bba2e32a1e9a1a760
    20 Nf79363c39f604734bd32cf842e59e5e7
    21 sg:journal.1136220
    22 schema:name Gamma-convergence of nonlocal perimeter functionals
    23 schema:pagination 377-403
    24 schema:productId N02f523d2dcb94178b798055a7ced7cbf
    25 N6585bb84b7aa4cd3a57ff2faf960f85c
    26 Ne03a11a5cae04db795d10fbe57c5361a
    27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051699194
    28 https://doi.org/10.1007/s00229-010-0399-4
    29 schema:sdDatePublished 2019-04-10T16:43
    30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    31 schema:sdPublisher N957df1295a8449aa950a5bbd9b714fbf
    32 schema:url http://link.springer.com/10.1007%2Fs00229-010-0399-4
    33 sgo:license sg:explorer/license/
    34 sgo:sdDataset articles
    35 rdf:type schema:ScholarlyArticle
    36 N02f523d2dcb94178b798055a7ced7cbf schema:name dimensions_id
    37 schema:value pub.1051699194
    38 rdf:type schema:PropertyValue
    39 N1c8620dff23949a5a776ca89ced3028b schema:affiliation Nc4c6b4eb8a844829acf8ffb6a1839c90
    40 schema:familyName Martinazzi
    41 schema:givenName Luca
    42 rdf:type schema:Person
    43 N4cfed65af2714f5bba2e32a1e9a1a760 schema:issueNumber 3-4
    44 rdf:type schema:PublicationIssue
    45 N6585bb84b7aa4cd3a57ff2faf960f85c schema:name readcube_id
    46 schema:value f644cae1779c97fe82945c751b82b52522696c577da70cdc307d06a39e6f9a91
    47 rdf:type schema:PropertyValue
    48 N7342a0f90a434b6eb61c9424fdce36d1 rdf:first sg:person.012621721115.68
    49 rdf:rest N9ede3724bbc9497390a55acb475ced29
    50 N79776ad60f804229a9a14c817ab9670b rdf:first N1c8620dff23949a5a776ca89ced3028b
    51 rdf:rest rdf:nil
    52 N957df1295a8449aa950a5bbd9b714fbf schema:name Springer Nature - SN SciGraph project
    53 rdf:type schema:Organization
    54 N9ede3724bbc9497390a55acb475ced29 rdf:first sg:person.011510274777.31
    55 rdf:rest N79776ad60f804229a9a14c817ab9670b
    56 Nc4c6b4eb8a844829acf8ffb6a1839c90 schema:name Centro De Giorgi, Pisa, Italy
    57 rdf:type schema:Organization
    58 Ne03a11a5cae04db795d10fbe57c5361a schema:name doi
    59 schema:value 10.1007/s00229-010-0399-4
    60 rdf:type schema:PropertyValue
    61 Nf79363c39f604734bd32cf842e59e5e7 schema:volumeNumber 134
    62 rdf:type schema:PublicationVolume
    63 anzsrc-for:16 schema:inDefinedTermSet anzsrc-for:
    64 schema:name Studies in Human Society
    65 rdf:type schema:DefinedTerm
    66 anzsrc-for:1608 schema:inDefinedTermSet anzsrc-for:
    67 schema:name Sociology
    68 rdf:type schema:DefinedTerm
    69 sg:journal.1136220 schema:issn 0025-2611
    70 1432-1785
    71 schema:name manuscripta mathematica
    72 rdf:type schema:Periodical
    73 sg:person.011510274777.31 schema:affiliation https://www.grid.ac/institutes/grid.6093.c
    74 schema:familyName Philippis
    75 schema:givenName Guido De
    76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011510274777.31
    77 rdf:type schema:Person
    78 sg:person.012621721115.68 schema:affiliation https://www.grid.ac/institutes/grid.6093.c
    79 schema:familyName Ambrosio
    80 schema:givenName Luigi
    81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68
    82 rdf:type schema:Person
    83 sg:pub.10.1007/978-1-4684-9486-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006563782
    84 https://doi.org/10.1007/978-1-4684-9486-0
    85 rdf:type schema:CreativeWork
    86 sg:pub.10.1007/bf03167679 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045616123
    87 https://doi.org/10.1007/bf03167679
    88 rdf:type schema:CreativeWork
    89 sg:pub.10.1007/s00526-010-0359-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017063594
    90 https://doi.org/10.1007/s00526-010-0359-6
    91 rdf:type schema:CreativeWork
    92 https://app.dimensions.ai/details/publication/pub.1013789647 schema:CreativeWork
    93 https://doi.org/10.1002/cpa.20331 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011323931
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.1016/s0022-1236(03)00002-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048812310
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.1090/s0002-9947-1947-0020618-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008281265
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1137/0523060 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062848473
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.4171/jems/108 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072317680
    102 rdf:type schema:CreativeWork
    103 https://www.grid.ac/institutes/grid.6093.c schema:alternateName Scuola Normale Superiore di Pisa
    104 schema:name Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy
    105 rdf:type schema:Organization
     




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


    ...