The behavior of the best Sobolev trace constant and extremals in thin domains

Autores
Fernández Bonder, J.; Martínez, S.; Rossi, J.D.
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved.
Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Differ. Equ. 2004;198(1):129-148
Materia
Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_00220396_v198_n1_p129_FernandezBonder
Acceder
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oai_identifier_str paperaa:paper_00220396_v198_n1_p129_FernandezBonder
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling The behavior of the best Sobolev trace constant and extremals in thin domainsFernández Bonder, J.Martínez, S.Rossi, J.D.Eigenvalue problemsNonlinear boundary conditionsp-LaplacianSobolev trace constantsIn this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved.Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonderJ. Differ. Equ. 2004;198(1):129-148reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-30T11:21:01Zpaperaa:paper_00220396_v198_n1_p129_FernandezBonderInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-30 11:21:02.592Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv The behavior of the best Sobolev trace constant and extremals in thin domains
title The behavior of the best Sobolev trace constant and extremals in thin domains
spellingShingle The behavior of the best Sobolev trace constant and extremals in thin domains
Fernández Bonder, J.
Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
title_short The behavior of the best Sobolev trace constant and extremals in thin domains
title_full The behavior of the best Sobolev trace constant and extremals in thin domains
title_fullStr The behavior of the best Sobolev trace constant and extremals in thin domains
title_full_unstemmed The behavior of the best Sobolev trace constant and extremals in thin domains
title_sort The behavior of the best Sobolev trace constant and extremals in thin domains
dc.creator.none.fl_str_mv Fernández Bonder, J.
Martínez, S.
Rossi, J.D.
author Fernández Bonder, J.
author_facet Fernández Bonder, J.
Martínez, S.
Rossi, J.D.
author_role author
author2 Martínez, S.
Rossi, J.D.
author2_role author
author
dc.subject.none.fl_str_mv Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
topic Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
dc.description.none.fl_txt_mv In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved.
Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved.
publishDate 2004
dc.date.none.fl_str_mv 2004
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/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
url http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Differ. Equ. 2004;198(1):129-148
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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