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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/144405
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oai:ri.conicet.gov.ar:11336/144405 |
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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 Técnicas2025-09-29T10:28:03Zoai: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:34982025-09-29 10:28:03.371CONICET 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 |
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1844614283850153984 |
score |
13.070432 |