The best Sobolev trace constant in domains with holes for critical or subcritical exponents

Autores
Fernandez Bonder, Julian; Orive, R.; Rossi, Julio Daniel
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary.
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, R.. 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
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:11336/127509
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/127509
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The best Sobolev trace constant in domains with holes for critical or subcritical exponentsFernandez Bonder, JulianOrive, R.Rossi, Julio DanielHOMOGENIZATIONNONLINEAR BOUNDARY CONDITIONSSOBOLEV TRACE EMBEDDING.https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary.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, R.. 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"; ArgentinaCambridge University Press2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/127509Fernandez Bonder, Julian; Orive, R.; Rossi, Julio Daniel; The best Sobolev trace constant in domains with holes for critical or subcritical exponents; Cambridge University Press; Anziam Journal; 49; 2; 12-2007; 213-2301446-1811CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S1446181100012797info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/anziam-journal/article/best-sobolev-trace-constant-in-domains-with-holes-for-critical-or-subcritical-exponents/FF3AF25067DE3B6ED051BB59D0D61F0Ainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:54:34Zoai:ri.conicet.gov.ar:11336/127509instacron: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:34982025-09-03 09:54:35.218CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The best Sobolev trace constant in domains with holes for critical or subcritical exponents
title The best Sobolev trace constant in domains with holes for critical or subcritical exponents
spellingShingle The best Sobolev trace constant in domains with holes for critical or subcritical exponents
Fernandez Bonder, Julian
HOMOGENIZATION
NONLINEAR BOUNDARY CONDITIONS
SOBOLEV TRACE EMBEDDING.
title_short The best Sobolev trace constant in domains with holes for critical or subcritical exponents
title_full The best Sobolev trace constant in domains with holes for critical or subcritical exponents
title_fullStr The best Sobolev trace constant in domains with holes for critical or subcritical exponents
title_full_unstemmed The best Sobolev trace constant in domains with holes for critical or subcritical exponents
title_sort The best Sobolev trace constant in domains with holes for critical or subcritical exponents
dc.creator.none.fl_str_mv Fernandez Bonder, Julian
Orive, R.
Rossi, Julio Daniel
author Fernandez Bonder, Julian
author_facet Fernandez Bonder, Julian
Orive, R.
Rossi, Julio Daniel
author_role author
author2 Orive, R.
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 the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary.
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, R.. 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 the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary.
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/11336/127509
Fernandez Bonder, Julian; Orive, R.; Rossi, Julio Daniel; The best Sobolev trace constant in domains with holes for critical or subcritical exponents; Cambridge University Press; Anziam Journal; 49; 2; 12-2007; 213-230
1446-1811
CONICET Digital
CONICET
url http://hdl.handle.net/11336/127509
identifier_str_mv Fernandez Bonder, Julian; Orive, R.; Rossi, Julio Daniel; The best Sobolev trace constant in domains with holes for critical or subcritical exponents; Cambridge University Press; Anziam Journal; 49; 2; 12-2007; 213-230
1446-1811
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/S1446181100012797
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/anziam-journal/article/best-sobolev-trace-constant-in-domains-with-holes-for-critical-or-subcritical-exponents/FF3AF25067DE3B6ED051BB59D0D61F0A
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 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
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score 13.13397

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