On the best Sobolev trace constant and extremals in domains with holes

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We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measu...

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Autores principales: Fernández Bonder, J., Rossi, J.D., Wolanski, N.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2006
Materias:
Eigenvalue optimization problems
p-capacity
p-Laplacian
Sobolev trace constant
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_00074497_v130_n7_p565_FernandezBonder
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spelling paperaa:paper_00074497_v130_n7_p565_FernandezBonder2023-06-12T16:41:22Z On the best Sobolev trace constant and extremals in domains with holes Bull. Sci. Math. 2006;130(7):565-579 Fernández Bonder, J. Rossi, J.D. Wolanski, N. Eigenvalue optimization problems p-capacity p-Laplacian Sobolev trace constant We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p = 2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. © 2005 Elsevier SAS. All rights reserved. Fil:Fernández Bonder, J. 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. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Eigenvalue optimization problems
p-capacity
p-Laplacian
Sobolev trace constant
spellingShingle Eigenvalue optimization problems
p-capacity
p-Laplacian
Sobolev trace constant
Fernández Bonder, J.
Rossi, J.D.
Wolanski, N.
On the best Sobolev trace constant and extremals in domains with holes
topic_facet Eigenvalue optimization problems
p-capacity
p-Laplacian
Sobolev trace constant
description We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p = 2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. © 2005 Elsevier SAS. All rights reserved.
format Artículo
Artículo
publishedVersion
author Fernández Bonder, J.
Rossi, J.D.
Wolanski, N.
author_facet Fernández Bonder, J.
Rossi, J.D.
Wolanski, N.
author_sort Fernández Bonder, J.
title On the best Sobolev trace constant and extremals in domains with holes
title_short On the best Sobolev trace constant and extremals in domains with holes
title_full On the best Sobolev trace constant and extremals in domains with holes
title_fullStr On the best Sobolev trace constant and extremals in domains with holes
title_full_unstemmed On the best Sobolev trace constant and extremals in domains with holes
title_sort on the best sobolev trace constant and extremals in domains with holes
publishDate 2006
url http://hdl.handle.net/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonder
work_keys_str_mv AT fernandezbonderj onthebestsobolevtraceconstantandextremalsindomainswithholes
AT rossijd onthebestsobolevtraceconstantandextremalsindomainswithholes
AT wolanskin onthebestsobolevtraceconstantandextremalsindomainswithholes
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