Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN

Autores
Saintier, Nicolas Bernard Claude; Silva, Analia
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity.
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis ; Argentina
Materia
CONCENTRATION COMPACTNESS
CRITICAL EXPONENTS
SOBOLEV EMBEDDING
VARIABLE EXPONENTS
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:11336/60103
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RNSaintier, Nicolas Bernard ClaudeSilva, AnaliaCONCENTRATION COMPACTNESSCRITICAL EXPONENTSSOBOLEV EMBEDDINGVARIABLE EXPONENTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity.Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis ; ArgentinaSpringer2017-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60103Saintier, Nicolas Bernard Claude; Silva, Analia; Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN; Springer; Nonlinear Differential Equations And Applications; 24; 2; 4-2017; 1-301021-97221420-9004CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00030-017-0441-2info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00030-017-0441-2info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.04574info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:05:48Zoai:ri.conicet.gov.ar:11336/60103instacron: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:34982025-10-29 12:05:48.685CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
spellingShingle Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
Saintier, Nicolas Bernard Claude
CONCENTRATION COMPACTNESS
CRITICAL EXPONENTS
SOBOLEV EMBEDDING
VARIABLE EXPONENTS
title_short Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_full Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_fullStr Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_full_unstemmed Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_sort Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
dc.creator.none.fl_str_mv Saintier, Nicolas Bernard Claude
Silva, Analia
author Saintier, Nicolas Bernard Claude
author_facet Saintier, Nicolas Bernard Claude
Silva, Analia
author_role author
author2 Silva, Analia
author2_role author
dc.subject.none.fl_str_mv CONCENTRATION COMPACTNESS
CRITICAL EXPONENTS
SOBOLEV EMBEDDING
VARIABLE EXPONENTS
topic CONCENTRATION COMPACTNESS
CRITICAL EXPONENTS
SOBOLEV EMBEDDING
VARIABLE EXPONENTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity.
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Silva, Analia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis ; Argentina
description The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity.
publishDate 2017
dc.date.none.fl_str_mv 2017-04
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/11336/60103
Saintier, Nicolas Bernard Claude; Silva, Analia; Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN; Springer; Nonlinear Differential Equations And Applications; 24; 2; 4-2017; 1-30
1021-9722
1420-9004
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60103
identifier_str_mv Saintier, Nicolas Bernard Claude; Silva, Analia; Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN; Springer; Nonlinear Differential Equations And Applications; 24; 2; 4-2017; 1-30
1021-9722
1420-9004
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00030-017-0441-2
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00030-017-0441-2
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1511.04574
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
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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score 13.10058

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