Optimal boundary holes for the Sobolev trace constant
- Autores
- del Pezzo, Leandro Martin; Fernandez Bonder, Julian; Neves, Wladimir
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set.
Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Fernandez Bonder, Julian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Neves, Wladimir. Universidade Federal Do Rio de Janeiro; Brasil - Materia
-
Steklov eigenvalues
p-laplace operator
shape optimization - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/14928
Ver los metadatos del registro completo
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Optimal boundary holes for the Sobolev trace constantdel Pezzo, Leandro MartinFernandez Bonder, JulianNeves, WladimirSteklov eigenvaluesp-laplace operatorshape optimizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set.Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Fernandez Bonder, Julian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Neves, Wladimir. Universidade Federal Do Rio de Janeiro; BrasilElsevier2011-07-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14928del Pezzo, Leandro Martin; Fernandez Bonder, Julian; Neves, Wladimir; Optimal boundary holes for the Sobolev trace constant; Elsevier; Journal Of Differential Equations; 251; 8; 21-7-2011; 2327-23510022-0396enginfo:eu-repo/semantics/altIdentifier/doi/doi:10.1016/j.jde.2011.07.006info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022039611002579?via%3Dihubinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:28Zoai:ri.conicet.gov.ar:11336/14928instacron: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 09:48:28.565CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Optimal boundary holes for the Sobolev trace constant |
title |
Optimal boundary holes for the Sobolev trace constant |
spellingShingle |
Optimal boundary holes for the Sobolev trace constant del Pezzo, Leandro Martin Steklov eigenvalues p-laplace operator shape optimization |
title_short |
Optimal boundary holes for the Sobolev trace constant |
title_full |
Optimal boundary holes for the Sobolev trace constant |
title_fullStr |
Optimal boundary holes for the Sobolev trace constant |
title_full_unstemmed |
Optimal boundary holes for the Sobolev trace constant |
title_sort |
Optimal boundary holes for the Sobolev trace constant |
dc.creator.none.fl_str_mv |
del Pezzo, Leandro Martin Fernandez Bonder, Julian Neves, Wladimir |
author |
del Pezzo, Leandro Martin |
author_facet |
del Pezzo, Leandro Martin Fernandez Bonder, Julian Neves, Wladimir |
author_role |
author |
author2 |
Fernandez Bonder, Julian Neves, Wladimir |
author2_role |
author author |
dc.subject.none.fl_str_mv |
Steklov eigenvalues p-laplace operator shape optimization |
topic |
Steklov eigenvalues p-laplace operator shape optimization |
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 problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. Fil: del Pezzo, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina Fil: Fernandez Bonder, Julian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Neves, Wladimir. Universidade Federal Do Rio de Janeiro; Brasil |
description |
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-07-21 |
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/11336/14928 del Pezzo, Leandro Martin; Fernandez Bonder, Julian; Neves, Wladimir; Optimal boundary holes for the Sobolev trace constant; Elsevier; Journal Of Differential Equations; 251; 8; 21-7-2011; 2327-2351 0022-0396 |
url |
http://hdl.handle.net/11336/14928 |
identifier_str_mv |
del Pezzo, Leandro Martin; Fernandez Bonder, Julian; Neves, Wladimir; Optimal boundary holes for the Sobolev trace constant; Elsevier; Journal Of Differential Equations; 251; 8; 21-7-2011; 2327-2351 0022-0396 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/doi:10.1016/j.jde.2011.07.006 info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022039611002579?via%3Dihub |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1844613505152450560 |
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13.070432 |