Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy

Autores
Medina, Maria; Ochoa, Pablo Daniel
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations.
Fil: Medina, Maria. Universidad Autónoma de Madrid; España
Fil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería; Argentina
Materia
COMPARISON PRINCIPLE
NONLINEAR ELLIPTIC EQUATIONS
P(X)-LAPLACIAN
VISCOSITY SOLUTIONS
WEAK SOLUTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/219037
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Equivalence of solutions for non-homogeneous p(x)-Laplace equationsyMedina, MariaOchoa, Pablo DanielCOMPARISON PRINCIPLENONLINEAR ELLIPTIC EQUATIONSP(X)-LAPLACIANVISCOSITY SOLUTIONSWEAK SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations.Fil: Medina, Maria. Universidad Autónoma de Madrid; EspañaFil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería; ArgentinaAmerican Institute of Mathematical Sciences2023-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/219037Medina, Maria; Ochoa, Pablo Daniel; Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy; American Institute of Mathematical Sciences; Mathematics in Engineering; 5; 2; 1-2023; 1-192640-3501CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/mine.2023044info:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/article/doi/10.3934/mine.2023044?viewType=HTMLinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:09:11Zoai:ri.conicet.gov.ar:11336/219037instacron: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:34982025-09-10 13:09:11.786CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
title Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
spellingShingle Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
Medina, Maria
COMPARISON PRINCIPLE
NONLINEAR ELLIPTIC EQUATIONS
P(X)-LAPLACIAN
VISCOSITY SOLUTIONS
WEAK SOLUTIONS
title_short Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
title_full Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
title_fullStr Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
title_full_unstemmed Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
title_sort Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
dc.creator.none.fl_str_mv Medina, Maria
Ochoa, Pablo Daniel
author Medina, Maria
author_facet Medina, Maria
Ochoa, Pablo Daniel
author_role author
author2 Ochoa, Pablo Daniel
author2_role author
dc.subject.none.fl_str_mv COMPARISON PRINCIPLE
NONLINEAR ELLIPTIC EQUATIONS
P(X)-LAPLACIAN
VISCOSITY SOLUTIONS
WEAK SOLUTIONS
topic COMPARISON PRINCIPLE
NONLINEAR ELLIPTIC EQUATIONS
P(X)-LAPLACIAN
VISCOSITY SOLUTIONS
WEAK SOLUTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations.
Fil: Medina, Maria. Universidad Autónoma de Madrid; España
Fil: Ochoa, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ingeniería; Argentina
description We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations.
publishDate 2023
dc.date.none.fl_str_mv 2023-01
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/11336/219037
Medina, Maria; Ochoa, Pablo Daniel; Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy; American Institute of Mathematical Sciences; Mathematics in Engineering; 5; 2; 1-2023; 1-19
2640-3501
CONICET Digital
CONICET
url http://hdl.handle.net/11336/219037
identifier_str_mv Medina, Maria; Ochoa, Pablo Daniel; Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy; American Institute of Mathematical Sciences; Mathematics in Engineering; 5; 2; 1-2023; 1-19
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/doi/10.3934/mine.2023044
info:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/article/doi/10.3934/mine.2023044?viewType=HTML
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/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_ 1842980447083036672
score 13.004268

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