Entropy solutions for the $p(x)$-Laplace equations

We consider a Dirichlet problem in divergence form with variable growth, modeled on the $ p(x)$-Laplace equation. We obtain existence and uniqueness of an entropy solution for $ L^1$ data, as well as integrability results for the solution and its gradient. The proofs rely crucially on a priori estim...

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Detalles Bibliográficos
Autores: Sanchón, Manel, Urbano, José Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/96448
Acceso en línea:https://hdl.handle.net/2445/96448
Access Level:acceso abierto
Palabra clave:Equacions en derivades parcials
Operadors el·líptics
Anàlisi funcional no lineal
Partial differential equations
Elliptic operator
Nonlinear functional analysis
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spelling Entropy solutions for the $p(x)$-Laplace equationsSanchón, ManelUrbano, José MiguelEquacions en derivades parcialsOperadors el·lípticsAnàlisi funcional no linealPartial differential equationsElliptic operatorNonlinear functional analysisWe consider a Dirichlet problem in divergence form with variable growth, modeled on the $ p(x)$-Laplace equation. We obtain existence and uniqueness of an entropy solution for $ L^1$ data, as well as integrability results for the solution and its gradient. The proofs rely crucially on a priori estimates in Marcinkiewicz spaces with variable exponent, for which we obtain new inclusion results of independent interest.American Mathematical Society (AMS)2016201620092016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion19 p.application/pdfhttps://hdl.handle.net/2445/96448Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-09-04399-2Transactions of the American Mathematical Society, 2009, vol. 361, num. 12, p. 6387-6405http://dx.doi.org/10.1090/S0002-9947-09-04399-2(c) American Mathematical Society (AMS), 2009info:eu-repo/semantics/openAccessoai:recercat.cat:2445/964482026-05-29T05:05:01Z
dc.title.none.fl_str_mv Entropy solutions for the $p(x)$-Laplace equations
title Entropy solutions for the $p(x)$-Laplace equations
spellingShingle Entropy solutions for the $p(x)$-Laplace equations
Sanchón, Manel
Equacions en derivades parcials
Operadors el·líptics
Anàlisi funcional no lineal
Partial differential equations
Elliptic operator
Nonlinear functional analysis
title_short Entropy solutions for the $p(x)$-Laplace equations
title_full Entropy solutions for the $p(x)$-Laplace equations
title_fullStr Entropy solutions for the $p(x)$-Laplace equations
title_full_unstemmed Entropy solutions for the $p(x)$-Laplace equations
title_sort Entropy solutions for the $p(x)$-Laplace equations
dc.creator.none.fl_str_mv Sanchón, Manel
Urbano, José Miguel
author Sanchón, Manel
author_facet Sanchón, Manel
Urbano, José Miguel
author_role author
author2 Urbano, José Miguel
author2_role author
dc.subject.none.fl_str_mv Equacions en derivades parcials
Operadors el·líptics
Anàlisi funcional no lineal
Partial differential equations
Elliptic operator
Nonlinear functional analysis
topic Equacions en derivades parcials
Operadors el·líptics
Anàlisi funcional no lineal
Partial differential equations
Elliptic operator
Nonlinear functional analysis
description We consider a Dirichlet problem in divergence form with variable growth, modeled on the $ p(x)$-Laplace equation. We obtain existence and uniqueness of an entropy solution for $ L^1$ data, as well as integrability results for the solution and its gradient. The proofs rely crucially on a priori estimates in Marcinkiewicz spaces with variable exponent, for which we obtain new inclusion results of independent interest.
publishDate 2009
dc.date.none.fl_str_mv 2009
2016
2016
2016
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/2445/96448
url https://hdl.handle.net/2445/96448
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-09-04399-2
Transactions of the American Mathematical Society, 2009, vol. 361, num. 12, p. 6387-6405
http://dx.doi.org/10.1090/S0002-9947-09-04399-2
dc.rights.none.fl_str_mv (c) American Mathematical Society (AMS), 2009
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Mathematical Society (AMS), 2009
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19 p.
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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