Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients

This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using a pointwise estimate of the solutions combined with a two-dimensional capaci...

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Detalles Bibliográficos
Autores: Briane, Marc, Casado Díaz, Juan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/138410
Acceso en línea:https://hdl.handle.net/11441/138410
https://doi.org/10.1016/j.jde.2008.07.027
Access Level:acceso abierto
Palabra clave:Linear degenerate elliptic equations
Continuity of solutions
Uniform convergence of solutions
Maximum principle
Homogenization
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spelling Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficientsBriane, MarcCasado Díaz, JuanLinear degenerate elliptic equationsContinuity of solutionsUniform convergence of solutionsMaximum principleHomogenizationThis paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using a pointwise estimate of the solutions combined with a two-dimensional capacitary estimate. We give two applications of this result: the continuity of the solutions of two-dimensional linear elliptic equations by a constructive approach, and the density of the continuous functions in the domain of the Γ-limit of equicoercive diffusion energies in dimension two. We also build two counter-examples which show that the previous results cannot be extended to dimension three.ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/138410https://doi.org/10.1016/j.jde.2008.07.027reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Differential Equations, 245 (8), 2038-2054.https://doi.org/10.1016/j.jde.2008.07.027info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1384102026-06-17T12:51:07Z
dc.title.none.fl_str_mv Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
title Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
spellingShingle Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
Briane, Marc
Linear degenerate elliptic equations
Continuity of solutions
Uniform convergence of solutions
Maximum principle
Homogenization
title_short Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
title_full Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
title_fullStr Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
title_full_unstemmed Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
title_sort Uniform convergence of sequences of solutions of two-dimensional linear elliptic equations with unbounded coefficients
dc.creator.none.fl_str_mv Briane, Marc
Casado Díaz, Juan
author Briane, Marc
author_facet Briane, Marc
Casado Díaz, Juan
author_role author
author2 Casado Díaz, Juan
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
dc.subject.none.fl_str_mv Linear degenerate elliptic equations
Continuity of solutions
Uniform convergence of solutions
Maximum principle
Homogenization
topic Linear degenerate elliptic equations
Continuity of solutions
Uniform convergence of solutions
Maximum principle
Homogenization
description This paper deals with the behavior of two-dimensional linear elliptic equations with unbounded (and possibly infinite) coefficients. We prove the uniform convergence of the solutions by truncating the coefficients and using a pointwise estimate of the solutions combined with a two-dimensional capacitary estimate. We give two applications of this result: the continuity of the solutions of two-dimensional linear elliptic equations by a constructive approach, and the density of the continuous functions in the domain of the Γ-limit of equicoercive diffusion energies in dimension two. We also build two counter-examples which show that the previous results cannot be extended to dimension three.
publishDate 2008
dc.date.none.fl_str_mv 2008
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/138410
https://doi.org/10.1016/j.jde.2008.07.027
url https://hdl.handle.net/11441/138410
https://doi.org/10.1016/j.jde.2008.07.027
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Differential Equations, 245 (8), 2038-2054.
https://doi.org/10.1016/j.jde.2008.07.027
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
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