The best Sobolev trace constant in periodic media for critical and subcritical exponents

Autores
Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aɛ(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).
Fil: Fernandez Bonder, Julian. 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: Orive, Rafael. Universidad Autónoma de Madrid; España
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
HOMOGENIZATION
NONLINEAR BOUNDARY CONDITIONS
SOBOLEV TRACE EMBEDDING
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:11336/154860
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The best Sobolev trace constant in periodic media for critical and subcritical exponentsFernandez Bonder, JulianOrive, RafaelRossi, Julio DanielHOMOGENIZATIONNONLINEAR BOUNDARY CONDITIONSSOBOLEV TRACE EMBEDDINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aɛ(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).Fil: Fernandez Bonder, Julian. 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: Orive, Rafael. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaCambridge University Press2009-09info: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/11336/154860Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in periodic media for critical and subcritical exponents; Cambridge University Press; Glasgow Mathematical Journal; 51; 3; 9-2009; 619-6300017-0895CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0017089509990048info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:18Zoai:ri.conicet.gov.ar:11336/154860instacron: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 09:56:19.117CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The best Sobolev trace constant in periodic media for critical and subcritical exponents
title The best Sobolev trace constant in periodic media for critical and subcritical exponents
spellingShingle The best Sobolev trace constant in periodic media for critical and subcritical exponents
Fernandez Bonder, Julian
HOMOGENIZATION
NONLINEAR BOUNDARY CONDITIONS
SOBOLEV TRACE EMBEDDING
title_short The best Sobolev trace constant in periodic media for critical and subcritical exponents
title_full The best Sobolev trace constant in periodic media for critical and subcritical exponents
title_fullStr The best Sobolev trace constant in periodic media for critical and subcritical exponents
title_full_unstemmed The best Sobolev trace constant in periodic media for critical and subcritical exponents
title_sort The best Sobolev trace constant in periodic media for critical and subcritical exponents
dc.creator.none.fl_str_mv Fernandez Bonder, Julian
Orive, Rafael
Rossi, Julio Daniel
author Fernandez Bonder, Julian
author_facet Fernandez Bonder, Julian
Orive, Rafael
Rossi, Julio Daniel
author_role author
author2 Orive, Rafael
Rossi, Julio Daniel
author2_role author
author
dc.subject.none.fl_str_mv HOMOGENIZATION
NONLINEAR BOUNDARY CONDITIONS
SOBOLEV TRACE EMBEDDING
topic HOMOGENIZATION
NONLINEAR BOUNDARY CONDITIONS
SOBOLEV TRACE EMBEDDING
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 study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aɛ(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).
Fil: Fernandez Bonder, Julian. 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: Orive, Rafael. Universidad Autónoma de Madrid; España
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aɛ(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).
publishDate 2009
dc.date.none.fl_str_mv 2009-09
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/11336/154860
Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in periodic media for critical and subcritical exponents; Cambridge University Press; Glasgow Mathematical Journal; 51; 3; 9-2009; 619-630
0017-0895
CONICET Digital
CONICET
url http://hdl.handle.net/11336/154860
identifier_str_mv Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in periodic media for critical and subcritical exponents; Cambridge University Press; Glasgow Mathematical Journal; 51; 3; 9-2009; 619-630
0017-0895
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0017089509990048
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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_ 1844613692591702016
score 13.070432

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