The best Sobolev trace constant in a domain with oscillating boundary

Autores
Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations.
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. 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
HOMOGENIZATION
SOBOLEV TRACE EMBEDDING
STEKLOV EIGENVALUES
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:11336/125781
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/125781
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The best Sobolev trace constant in a domain with oscillating boundaryFernandez Bonder, JulianOrive, RafaelRossi, Julio DanielHOMOGENIZATIONSOBOLEV TRACE EMBEDDINGSTEKLOV EIGENVALUEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations.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. 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"; ArgentinaPergamon-Elsevier Science Ltd2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125781Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in a domain with oscillating boundary; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 67; 4; 12-2007; 1173-11800362-546XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0362546X06004032info:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2006.07.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:15:52Zoai:ri.conicet.gov.ar:11336/125781instacron: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 13:15:52.28CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The best Sobolev trace constant in a domain with oscillating boundary
title The best Sobolev trace constant in a domain with oscillating boundary
spellingShingle The best Sobolev trace constant in a domain with oscillating boundary
Fernandez Bonder, Julian
HOMOGENIZATION
SOBOLEV TRACE EMBEDDING
STEKLOV EIGENVALUES
title_short The best Sobolev trace constant in a domain with oscillating boundary
title_full The best Sobolev trace constant in a domain with oscillating boundary
title_fullStr The best Sobolev trace constant in a domain with oscillating boundary
title_full_unstemmed The best Sobolev trace constant in a domain with oscillating boundary
title_sort The best Sobolev trace constant in a domain with oscillating boundary
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
SOBOLEV TRACE EMBEDDING
STEKLOV EIGENVALUES
topic HOMOGENIZATION
SOBOLEV TRACE EMBEDDING
STEKLOV EIGENVALUES
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 homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations.
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. 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 study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
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/11336/125781
Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in a domain with oscillating boundary; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 67; 4; 12-2007; 1173-1180
0362-546X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125781
identifier_str_mv Fernandez Bonder, Julian; Orive, Rafael; Rossi, Julio Daniel; The best Sobolev trace constant in a domain with oscillating boundary; Pergamon-Elsevier Science Ltd; Journal Of Nonlinear Analysis; 67; 4; 12-2007; 1173-1180
0362-546X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0362546X06004032
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.na.2006.07.005
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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 12.993085

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