Manifold constrained variational problems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1999-11

AUTHORS

B. Dacorogna, I. Fonseca, J. Malý, K. Trivisa

ABSTRACT

The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $C^1$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $m$\end{document}-dimensional manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{M}\subset \mathbb{ R}^d $\end{document} is obtained. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $f: \mathbb{ R}^{d \times N} \to [0, \infty)$\end{document} is a continuous function satisfying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $0 \le f(\xi) \le C (1 +{|\xi|}^p),$\end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ C > 0, \,p \geq 1,$\end{document} and for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\xi \in \mathbb{ R}^{d \times N},$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray} \mathcal{F}(u, \Omega) :&=& \inf_{\{u_n\}} \left\{\! \mathop{\rm inf}\limits_{\{ u_n\}} \int_\Omega f(\nabla u_n) \, dx: u_n \rightharpoonup u \, \mbox{in}\, \, W^{1,p}, \right. \nonumber && \left. u_n (x) \in \mathcal{M}\,\, \mbox{a.e.}\,\, x \in \Omega, n \in{\mathbb{N}} \! \right\}\nonumber &=& \int_\Omega Q_T f(u, \nabla u) \, dx, \nonumber \end{eqnarray} \end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Omega \subset \mathbb{ R}^N $\end{document} is open, bounded, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $Q_T f(y_0, \xi)$\end{document} is the tangential quasiconvexification of f at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $y_0 \in \mathcal{M},$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\xi = ({\xi}^1,...,{\xi}^N),{\xi}^i $\end{document} belong to the tangent space to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{M}$\end{document} at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $y_0,\, i=1,...,N.$\end{document} More... »

PAGES

185-206

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s005260050137

DOI

http://dx.doi.org/10.1007/s005260050137

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035924343


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/2008/2002", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Cultural Studies", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/20", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Language, Communication and Culture", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne", 
          "id": "https://www.grid.ac/institutes/grid.5333.6", 
          "name": [
            "D\u00e9partment de Math\u00e9matiques, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: bernard.dacorogna@epfl.ch), CH"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Dacorogna", 
        "givenName": "B.", 
        "id": "sg:person.013621604731.57", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013621604731.57"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Carnegie Mellon University", 
          "id": "https://www.grid.ac/institutes/grid.147455.6", 
          "name": [
            "Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: fonseca@andrew.cmu.edu), US"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fonseca", 
        "givenName": "I.", 
        "id": "sg:person.01003560110.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01003560110.78"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Charles University", 
          "id": "https://www.grid.ac/institutes/grid.4491.8", 
          "name": [
            "KMA Department, Faculty of Mathematics and Physics, Charles University, Sokolovsk\u00e1 83, CZ-186 75 Praha, Czech Republic (e-mail: maly@karlin.mff.cuni.cz), CZ"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mal\u00fd", 
        "givenName": "J.", 
        "id": "sg:person.016026347345.35", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016026347345.35"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Northwestern University", 
          "id": "https://www.grid.ac/institutes/grid.16753.36", 
          "name": [
            "Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston IL 60208, USA (e-mail: trivisa@math.nwu.edu), US"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Trivisa", 
        "givenName": "K.", 
        "id": "sg:person.07727432261.04", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07727432261.04"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1999-11", 
    "datePublishedReg": "1999-11-01", 
    "description": "The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $C^1$\\end{document}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $m$\\end{document}-dimensional manifold \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $\\mathcal{M}\\subset \\mathbb{ R}^d $\\end{document} is obtained. If \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $f: \\mathbb{ R}^{d \\times N} \\to [0, \\infty)$\\end{document} is a continuous function satisfying \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $0 \\le f(\\xi) \\le C (1 +{|\\xi|}^p),$\\end{document} for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $ C > 0, \\,p \\geq 1,$\\end{document} and for all \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $\\xi \\in \\mathbb{ R}^{d \\times N},$\\end{document} then \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{eqnarray} \\mathcal{F}(u, \\Omega) :&=& \\inf_{\\{u_n\\}} \\left\\{\\! \\mathop{\\rm inf}\\limits_{\\{ u_n\\}} \\int_\\Omega f(\\nabla u_n) \\, dx: u_n \\rightharpoonup u \\, \\mbox{in}\\, \\, W^{1,p}, \\right. \\nonumber && \\left. u_n (x) \\in \\mathcal{M}\\,\\, \\mbox{a.e.}\\,\\, x \\in \\Omega, n \\in{\\mathbb{N}} \\! \\right\\}\\nonumber &=& \\int_\\Omega Q_T f(u, \\nabla u) \\, dx, \\nonumber \\end{eqnarray} \\end{document} where \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $\\Omega \\subset \\mathbb{ R}^N $\\end{document} is open, bounded, and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $Q_T f(y_0, \\xi)$\\end{document} is the tangential quasiconvexification of f at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $y_0 \\in \\mathcal{M},$\\end{document}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $\\xi = ({\\xi}^1,...,{\\xi}^N),{\\xi}^i $\\end{document} belong to the tangent space to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $\\mathcal{M}$\\end{document} at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $y_0,\\, i=1,...,N.$\\end{document}", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s005260050137", 
    "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": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "9"
      }
    ], 
    "name": "Manifold constrained variational problems", 
    "pagination": "185-206", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "ab22022aaaa3a543a2f0ddf912e8e123d6cdcf08eb26183bf0c74308203e12b4"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s005260050137"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1035924343"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s005260050137", 
      "https://app.dimensions.ai/details/publication/pub.1035924343"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T16:46", 
    "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_00000533.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs005260050137"
  }
]
 

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/s005260050137'

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/s005260050137'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s005260050137'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s005260050137'


 

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

91 TRIPLES      20 PREDICATES      27 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s005260050137 schema:about anzsrc-for:20
2 anzsrc-for:2002
3 schema:author N407f487c034a41e09c26f536d83e26bf
4 schema:datePublished 1999-11
5 schema:datePublishedReg 1999-11-01
6 schema:description The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $C^1$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $m$\end{document}-dimensional manifold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{M}\subset \mathbb{ R}^d $\end{document} is obtained. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $f: \mathbb{ R}^{d \times N} \to [0, \infty)$\end{document} is a continuous function satisfying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $0 \le f(\xi) \le C (1 +{|\xi|}^p),$\end{document} for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ C > 0, \,p \geq 1,$\end{document} and for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\xi \in \mathbb{ R}^{d \times N},$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray} \mathcal{F}(u, \Omega) :&=& \inf_{\{u_n\}} \left\{\! \mathop{\rm inf}\limits_{\{ u_n\}} \int_\Omega f(\nabla u_n) \, dx: u_n \rightharpoonup u \, \mbox{in}\, \, W^{1,p}, \right. \nonumber && \left. u_n (x) \in \mathcal{M}\,\, \mbox{a.e.}\,\, x \in \Omega, n \in{\mathbb{N}} \! \right\}\nonumber &=& \int_\Omega Q_T f(u, \nabla u) \, dx, \nonumber \end{eqnarray} \end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Omega \subset \mathbb{ R}^N $\end{document} is open, bounded, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $Q_T f(y_0, \xi)$\end{document} is the tangential quasiconvexification of f at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $y_0 \in \mathcal{M},$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\xi = ({\xi}^1,...,{\xi}^N),{\xi}^i $\end{document} belong to the tangent space to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{M}$\end{document} at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $y_0,\, i=1,...,N.$\end{document}
7 schema:genre research_article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N78747a9e8d8e42198228c09c376b0ee3
11 N804f64b6fa8b4db08408b742fa2f7dba
12 sg:journal.1043284
13 schema:name Manifold constrained variational problems
14 schema:pagination 185-206
15 schema:productId N2f987b94aff9464d97727ab7556b5de5
16 N7ad9cbb0c48c4aa8b2209f48acd62514
17 N9194d761893f4dde9c22abee2142702d
18 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035924343
19 https://doi.org/10.1007/s005260050137
20 schema:sdDatePublished 2019-04-10T16:46
21 schema:sdLicense https://scigraph.springernature.com/explorer/license/
22 schema:sdPublisher Nefa21ac3210947eabaec9c1355450744
23 schema:url http://link.springer.com/10.1007%2Fs005260050137
24 sgo:license sg:explorer/license/
25 sgo:sdDataset articles
26 rdf:type schema:ScholarlyArticle
27 N17dff94a509d41558eeb13b103e535c1 rdf:first sg:person.01003560110.78
28 rdf:rest N7a1ba6ea4a8f460fbadaebdcdaa32678
29 N2f987b94aff9464d97727ab7556b5de5 schema:name readcube_id
30 schema:value ab22022aaaa3a543a2f0ddf912e8e123d6cdcf08eb26183bf0c74308203e12b4
31 rdf:type schema:PropertyValue
32 N407f487c034a41e09c26f536d83e26bf rdf:first sg:person.013621604731.57
33 rdf:rest N17dff94a509d41558eeb13b103e535c1
34 N78747a9e8d8e42198228c09c376b0ee3 schema:issueNumber 3
35 rdf:type schema:PublicationIssue
36 N7a1ba6ea4a8f460fbadaebdcdaa32678 rdf:first sg:person.016026347345.35
37 rdf:rest Nfc61f7a2748c4434bad8e9bdc2bd9887
38 N7ad9cbb0c48c4aa8b2209f48acd62514 schema:name dimensions_id
39 schema:value pub.1035924343
40 rdf:type schema:PropertyValue
41 N804f64b6fa8b4db08408b742fa2f7dba schema:volumeNumber 9
42 rdf:type schema:PublicationVolume
43 N9194d761893f4dde9c22abee2142702d schema:name doi
44 schema:value 10.1007/s005260050137
45 rdf:type schema:PropertyValue
46 Nefa21ac3210947eabaec9c1355450744 schema:name Springer Nature - SN SciGraph project
47 rdf:type schema:Organization
48 Nfc61f7a2748c4434bad8e9bdc2bd9887 rdf:first sg:person.07727432261.04
49 rdf:rest rdf:nil
50 anzsrc-for:20 schema:inDefinedTermSet anzsrc-for:
51 schema:name Language, Communication and Culture
52 rdf:type schema:DefinedTerm
53 anzsrc-for:2002 schema:inDefinedTermSet anzsrc-for:
54 schema:name Cultural Studies
55 rdf:type schema:DefinedTerm
56 sg:journal.1043284 schema:issn 0944-2669
57 1432-0835
58 schema:name Calculus of Variations and Partial Differential Equations
59 rdf:type schema:Periodical
60 sg:person.01003560110.78 schema:affiliation https://www.grid.ac/institutes/grid.147455.6
61 schema:familyName Fonseca
62 schema:givenName I.
63 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01003560110.78
64 rdf:type schema:Person
65 sg:person.013621604731.57 schema:affiliation https://www.grid.ac/institutes/grid.5333.6
66 schema:familyName Dacorogna
67 schema:givenName B.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013621604731.57
69 rdf:type schema:Person
70 sg:person.016026347345.35 schema:affiliation https://www.grid.ac/institutes/grid.4491.8
71 schema:familyName Malý
72 schema:givenName J.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016026347345.35
74 rdf:type schema:Person
75 sg:person.07727432261.04 schema:affiliation https://www.grid.ac/institutes/grid.16753.36
76 schema:familyName Trivisa
77 schema:givenName K.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07727432261.04
79 rdf:type schema:Person
80 https://www.grid.ac/institutes/grid.147455.6 schema:alternateName Carnegie Mellon University
81 schema:name Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA (e-mail: fonseca@andrew.cmu.edu), US
82 rdf:type schema:Organization
83 https://www.grid.ac/institutes/grid.16753.36 schema:alternateName Northwestern University
84 schema:name Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston IL 60208, USA (e-mail: trivisa@math.nwu.edu), US
85 rdf:type schema:Organization
86 https://www.grid.ac/institutes/grid.4491.8 schema:alternateName Charles University
87 schema:name KMA Department, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ-186 75 Praha, Czech Republic (e-mail: maly@karlin.mff.cuni.cz), CZ
88 rdf:type schema:Organization
89 https://www.grid.ac/institutes/grid.5333.6 schema:alternateName École Polytechnique Fédérale de Lausanne
90 schema:name Départment de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: bernard.dacorogna@epfl.ch), CH
91 rdf:type schema:Organization
 




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


...