Lipschitz continuity of minimizers in a problem with nonstandard growth

Autores
Lederman, Claudia Beatriz; Wolanski, Noemi Irene
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we obtain the Lipschitz continuity of nonnegative local minimizers of the functional J(v) = ∫ Ω - F(x; v; ∇v) + (x)νfv>0) dx, under nonstandard growth conditions of the energy function F(x; s; η) and 0 < λmin ≤ λ (x) ≤ λmax < 1. This is the optimal regularity for the problem. Our results generalize the ones we obtained in the case of the inhomogeneous p(x)-Laplacian in our previous work. Nonnegative local minimizers u satisfy in their positivity set a general nonlinear degenerate/singular equation divA(x; u; ∇u) = B(x; u; ru) of nonstandard growth type. As a by-product of our study, we obtain several results for this equation that are of independent interest.
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
FREE BOUNDARY PROBLEM
LIPSCHTIZ CONTINUITY
MINIMIZATION PROBLEM
NONLINEAR ELLIPTIC OPERATOR
NONSTANDARD GROWTH
P(X)-LAPLACIAN
SINGULAR AND DEGENERATE ELLIPTIC EQUATION
VARIABLE EXPONENT SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/144405
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/144405
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Lipschitz continuity of minimizers in a problem with nonstandard growthLederman, Claudia BeatrizWolanski, Noemi IreneFREE BOUNDARY PROBLEMLIPSCHTIZ CONTINUITYMINIMIZATION PROBLEMNONLINEAR ELLIPTIC OPERATORNONSTANDARD GROWTHP(X)-LAPLACIANSINGULAR AND DEGENERATE ELLIPTIC EQUATIONVARIABLE EXPONENT SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we obtain the Lipschitz continuity of nonnegative local minimizers of the functional J(v) = ∫ Ω - F(x; v; ∇v) + (x)νfv>0) dx, under nonstandard growth conditions of the energy function F(x; s; η) and 0 < λmin ≤ λ (x) ≤ λmax < 1. This is the optimal regularity for the problem. Our results generalize the ones we obtained in the case of the inhomogeneous p(x)-Laplacian in our previous work. Nonnegative local minimizers u satisfy in their positivity set a general nonlinear degenerate/singular equation divA(x; u; ∇u) = B(x; u; ru) of nonstandard growth type. As a by-product of our study, we obtain several results for this equation that are of independent interest.Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmerican Institute of Mathematical Sciences2020-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/144405Lederman, Claudia Beatriz; Wolanski, Noemi Irene; Lipschitz continuity of minimizers in a problem with nonstandard growth; American Institute of Mathematical Sciences; Mathematics In Engineering; 3; 1; 10-2020; 1-392640-3501CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/10.3934/mine.2021009info:eu-repo/semantics/altIdentifier/doi/10.3934/mine.2021009info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:00:26Zoai:ri.conicet.gov.ar:11336/144405instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 12:00:26.712CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Lipschitz continuity of minimizers in a problem with nonstandard growth
title Lipschitz continuity of minimizers in a problem with nonstandard growth
spellingShingle Lipschitz continuity of minimizers in a problem with nonstandard growth
Lederman, Claudia Beatriz
FREE BOUNDARY PROBLEM
LIPSCHTIZ CONTINUITY
MINIMIZATION PROBLEM
NONLINEAR ELLIPTIC OPERATOR
NONSTANDARD GROWTH
P(X)-LAPLACIAN
SINGULAR AND DEGENERATE ELLIPTIC EQUATION
VARIABLE EXPONENT SPACES
title_short Lipschitz continuity of minimizers in a problem with nonstandard growth
title_full Lipschitz continuity of minimizers in a problem with nonstandard growth
title_fullStr Lipschitz continuity of minimizers in a problem with nonstandard growth
title_full_unstemmed Lipschitz continuity of minimizers in a problem with nonstandard growth
title_sort Lipschitz continuity of minimizers in a problem with nonstandard growth
dc.creator.none.fl_str_mv Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author Lederman, Claudia Beatriz
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_role author
author2 Wolanski, Noemi Irene
author2_role author
dc.subject.none.fl_str_mv FREE BOUNDARY PROBLEM
LIPSCHTIZ CONTINUITY
MINIMIZATION PROBLEM
NONLINEAR ELLIPTIC OPERATOR
NONSTANDARD GROWTH
P(X)-LAPLACIAN
SINGULAR AND DEGENERATE ELLIPTIC EQUATION
VARIABLE EXPONENT SPACES
topic FREE BOUNDARY PROBLEM
LIPSCHTIZ CONTINUITY
MINIMIZATION PROBLEM
NONLINEAR ELLIPTIC OPERATOR
NONSTANDARD GROWTH
P(X)-LAPLACIAN
SINGULAR AND DEGENERATE ELLIPTIC EQUATION
VARIABLE EXPONENT SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we obtain the Lipschitz continuity of nonnegative local minimizers of the functional J(v) = ∫ Ω - F(x; v; ∇v) + (x)νfv>0) dx, under nonstandard growth conditions of the energy function F(x; s; η) and 0 < λmin ≤ λ (x) ≤ λmax < 1. This is the optimal regularity for the problem. Our results generalize the ones we obtained in the case of the inhomogeneous p(x)-Laplacian in our previous work. Nonnegative local minimizers u satisfy in their positivity set a general nonlinear degenerate/singular equation divA(x; u; ∇u) = B(x; u; ru) of nonstandard growth type. As a by-product of our study, we obtain several results for this equation that are of independent interest.
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper we obtain the Lipschitz continuity of nonnegative local minimizers of the functional J(v) = ∫ Ω - F(x; v; ∇v) + (x)νfv>0) dx, under nonstandard growth conditions of the energy function F(x; s; η) and 0 < λmin ≤ λ (x) ≤ λmax < 1. This is the optimal regularity for the problem. Our results generalize the ones we obtained in the case of the inhomogeneous p(x)-Laplacian in our previous work. Nonnegative local minimizers u satisfy in their positivity set a general nonlinear degenerate/singular equation divA(x; u; ∇u) = B(x; u; ru) of nonstandard growth type. As a by-product of our study, we obtain several results for this equation that are of independent interest.
publishDate 2020
dc.date.none.fl_str_mv 2020-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/144405
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; Lipschitz continuity of minimizers in a problem with nonstandard growth; American Institute of Mathematical Sciences; Mathematics In Engineering; 3; 1; 10-2020; 1-39
2640-3501
CONICET Digital
CONICET
url http://hdl.handle.net/11336/144405
identifier_str_mv Lederman, Claudia Beatriz; Wolanski, Noemi Irene; Lipschitz continuity of minimizers in a problem with nonstandard growth; American Institute of Mathematical Sciences; Mathematics In Engineering; 3; 1; 10-2020; 1-39
2640-3501
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/10.3934/mine.2021009
info:eu-repo/semantics/altIdentifier/doi/10.3934/mine.2021009
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846782331044495360
score 12.982451

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