Optimization problem for extremals of the trace inequality in domains with holes

Autores
del Pezzo, Leandro Martin
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.
Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Sobolev Trace Embedding
Shape Derivative
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:11336/16533
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/16533
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimization problem for extremals of the trace inequality in domains with holesdel Pezzo, Leandro MartinSobolev Trace EmbeddingShape DerivativeSteklov Eigenvalueshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWorld Scientific2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16533del Pezzo, Leandro Martin; Optimization problem for extremals of the trace inequality in domains with holes; World Scientific; Communications In Contemporary Mathematics; 12; 4; 8-2010; 569-5860219-19971793-6683enginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S0219199710003920info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0219199710003920info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0809.0246info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T11:16:21Zoai:ri.conicet.gov.ar:11336/16533instacron: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 11:16:21.512CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimization problem for extremals of the trace inequality in domains with holes
title Optimization problem for extremals of the trace inequality in domains with holes
spellingShingle Optimization problem for extremals of the trace inequality in domains with holes
del Pezzo, Leandro Martin
Sobolev Trace Embedding
Shape Derivative
Steklov Eigenvalues
title_short Optimization problem for extremals of the trace inequality in domains with holes
title_full Optimization problem for extremals of the trace inequality in domains with holes
title_fullStr Optimization problem for extremals of the trace inequality in domains with holes
title_full_unstemmed Optimization problem for extremals of the trace inequality in domains with holes
title_sort Optimization problem for extremals of the trace inequality in domains with holes
dc.creator.none.fl_str_mv del Pezzo, Leandro Martin
author del Pezzo, Leandro Martin
author_facet del Pezzo, Leandro Martin
author_role author
dc.subject.none.fl_str_mv Sobolev Trace Embedding
Shape Derivative
Steklov Eigenvalues
topic Sobolev Trace Embedding
Shape Derivative
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 We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.
Fil: del Pezzo, Leandro Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/16533
del Pezzo, Leandro Martin; Optimization problem for extremals of the trace inequality in domains with holes; World Scientific; Communications In Contemporary Mathematics; 12; 4; 8-2010; 569-586
0219-1997
1793-6683
url http://hdl.handle.net/11336/16533
identifier_str_mv del Pezzo, Leandro Martin; Optimization problem for extremals of the trace inequality in domains with holes; World Scientific; Communications In Contemporary Mathematics; 12; 4; 8-2010; 569-586
0219-1997
1793-6683
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219199710003920
info:eu-repo/semantics/altIdentifier/url/http://www.worldscientific.com/doi/abs/10.1142/S0219199710003920
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0809.0246
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 World Scientific
publisher.none.fl_str_mv World Scientific
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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