Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients

The present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over vector-valued functions in W1,p 0 (Ω)M , where p > 1, M ≥ 1, and Ω is a bounded open set of RN , N ≥ 2. The strongly local energy density Fn(·, Du) of the functional Fn satis...

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Detalles Bibliográficos
Autores: Briane, Marc, Casado Díaz, Juan, Luna Laynez, Manuel, Pallares Martín, Antonio Jesús
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/62394
Acceso en línea:http://hdl.handle.net/11441/62394
https://doi.org/10.1016/j.na.2016.11.009
Access Level:acceso abierto
Palabra clave:Γ-convergence
Nonlinear elliptic systems
Non-uniformly bounded coefficients
Hyperelasticity
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spelling Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficientsBriane, MarcCasado Díaz, JuanLuna Laynez, ManuelPallares Martín, Antonio JesúsΓ-convergenceNonlinear elliptic systemsNon-uniformly bounded coefficientsHyperelasticityThe present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over vector-valued functions in W1,p 0 (Ω)M , where p > 1, M ≥ 1, and Ω is a bounded open set of RN , N ≥ 2. The strongly local energy density Fn(·, Du) of the functional Fn satisfies a Lipschitz condition with respect to the second variable, which is controlled by a positive sequence {an} which is only bounded in some suitable space L r(Ω). We prove that the sequence {Fn} Γ-converges for the strong topology of Lp(Ω)M to a functional F which has a strongly local density F(·, Du) for sufficiently regular functions u. This compactness result extends former results on the topic, which are based either on maximum principle arguments in the nonlinear scalar case, or adapted div-curl lemmas in the linear case. Here, the vectorial character and the nonlinearity of the problem need a new approach based on a careful analysis of the asymptotic minimizers associated with the functional Fn. The relevance of the conditions which are imposed to the energy density Fn(·, Du), is illustrated by several examples including some classical hyper-elastic energies.Ministerio de Economía y CompetitividadInstitut de Recherche Mathématique de RennesElsevierEcuaciones Diferenciales y Análisis NuméricoFQM309: Control y Homogeneización de Ecuaciones en Derivadas ParcialesMinisterio de Economía y Competitividad (MINECO). EspañaInstitut de Recherche Mathématique de Rennes2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/62394https://doi.org/10.1016/j.na.2016.11.009reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Analysis: Theory, Methods & Applications, 151, 187-207.info:eu-repo/grantAgreement/MINECO/MTM2011-24457/http://ac.els-cdn.com/S0362546X16302899/1-s2.0-S0362546X16302899-main.pdf?_tid=e03fad62-66d5-11e7-8850-00000aacb35f&acdnat=1499845623_1fd704d628dd2fc57c204be3016b3656info:eu-repo/semantics/openAccessoai:idus.us.es:11441/623942026-06-17T12:51:07Z
dc.title.none.fl_str_mv Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
title Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
spellingShingle Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
Briane, Marc
Γ-convergence
Nonlinear elliptic systems
Non-uniformly bounded coefficients
Hyperelasticity
title_short Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
title_full Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
title_fullStr Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
title_full_unstemmed Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
title_sort Gamma-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients
dc.creator.none.fl_str_mv Briane, Marc
Casado Díaz, Juan
Luna Laynez, Manuel
Pallares Martín, Antonio Jesús
author Briane, Marc
author_facet Briane, Marc
Casado Díaz, Juan
Luna Laynez, Manuel
Pallares Martín, Antonio Jesús
author_role author
author2 Casado Díaz, Juan
Luna Laynez, Manuel
Pallares Martín, Antonio Jesús
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
Ministerio de Economía y Competitividad (MINECO). España
Institut de Recherche Mathématique de Rennes
dc.subject.none.fl_str_mv Γ-convergence
Nonlinear elliptic systems
Non-uniformly bounded coefficients
Hyperelasticity
topic Γ-convergence
Nonlinear elliptic systems
Non-uniformly bounded coefficients
Hyperelasticity
description The present paper deals with the asymptotic behavior of equi-coercive sequences {Fn} of nonlinear functionals defined over vector-valued functions in W1,p 0 (Ω)M , where p > 1, M ≥ 1, and Ω is a bounded open set of RN , N ≥ 2. The strongly local energy density Fn(·, Du) of the functional Fn satisfies a Lipschitz condition with respect to the second variable, which is controlled by a positive sequence {an} which is only bounded in some suitable space L r(Ω). We prove that the sequence {Fn} Γ-converges for the strong topology of Lp(Ω)M to a functional F which has a strongly local density F(·, Du) for sufficiently regular functions u. This compactness result extends former results on the topic, which are based either on maximum principle arguments in the nonlinear scalar case, or adapted div-curl lemmas in the linear case. Here, the vectorial character and the nonlinearity of the problem need a new approach based on a careful analysis of the asymptotic minimizers associated with the functional Fn. The relevance of the conditions which are imposed to the energy density Fn(·, Du), is illustrated by several examples including some classical hyper-elastic energies.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/62394
https://doi.org/10.1016/j.na.2016.11.009
url http://hdl.handle.net/11441/62394
https://doi.org/10.1016/j.na.2016.11.009
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Analysis: Theory, Methods & Applications, 151, 187-207.
info:eu-repo/grantAgreement/MINECO/MTM2011-24457/
http://ac.els-cdn.com/S0362546X16302899/1-s2.0-S0362546X16302899-main.pdf?_tid=e03fad62-66d5-11e7-8850-00000aacb35f&acdnat=1499845623_1fd704d628dd2fc57c204be3016b3656
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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