On the best Sobolev trace constant and extremals in domains with holes
- Autores
- Fernández Bonder, J.; Rossi, J.D.; Wolanski, N.
- Año de publicación
- 2006
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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. - Fuente
- Bull. Sci. Math. 2006;130(7):565-579
- Materia
-
Eigenvalue optimization problems
p-capacity
p-Laplacian
Sobolev trace constant - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/2.5/ar
- Repositorio
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- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_00074497_v130_n7_p565_FernandezBonder
Ver los metadatos del registro completo
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On the best Sobolev trace constant and extremals in domains with holesFernández Bonder, J.Rossi, J.D.Wolanski, N.Eigenvalue optimization problemsp-capacityp-LaplacianSobolev trace constantWe 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.2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonderBull. Sci. Math. 2006;130(7):565-579reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-11-27T08:37:06Zpaperaa:paper_00074497_v130_n7_p565_FernandezBonderInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-11-27 08:37:07.703Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse |
| dc.title.none.fl_str_mv |
On the best Sobolev trace constant and extremals in domains with holes |
| title |
On the best Sobolev trace constant and extremals in domains with holes |
| spellingShingle |
On the best Sobolev trace constant and extremals in domains with holes Fernández Bonder, J. Eigenvalue optimization problems p-capacity p-Laplacian Sobolev trace constant |
| 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 |
| dc.creator.none.fl_str_mv |
Fernández Bonder, J. Rossi, J.D. Wolanski, N. |
| author |
Fernández Bonder, J. |
| author_facet |
Fernández Bonder, J. Rossi, J.D. Wolanski, N. |
| author_role |
author |
| author2 |
Rossi, J.D. Wolanski, N. |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Eigenvalue optimization problems p-capacity p-Laplacian Sobolev trace constant |
| topic |
Eigenvalue optimization problems p-capacity p-Laplacian Sobolev trace constant |
| dc.description.none.fl_txt_mv |
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. |
| 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. |
| publishDate |
2006 |
| dc.date.none.fl_str_mv |
2006 |
| 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/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonder |
| url |
http://hdl.handle.net/20.500.12110/paper_00074497_v130_n7_p565_FernandezBonder |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar |
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openAccess |
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http://creativecommons.org/licenses/by/2.5/ar |
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application/pdf |
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Bull. Sci. Math. 2006;130(7):565-579 reponame:Biblioteca Digital (UBA-FCEN) instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales instacron:UBA-FCEN |
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Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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UBA-FCEN |
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Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
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ana@bl.fcen.uba.ar |
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