First variations of the best Sobolev trace constant with respect to the domain

In this paper we study the best constant of the Sobolev trace embedding H 1 (Ω) → L 2 (∂Ω), where Ω is a bounded smooth domain in ℝ N . We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we con...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Nonlinear boundary conditions
Sobolev trace embedding
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00084395_v51_n1_p140_Rossi
http://hdl.handle.net/20.500.12110/paper_00084395_v51_n1_p140_Rossi
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00084395_v51_n1_p140_Rossi
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spelling paper:paper_00084395_v51_n1_p140_Rossi2025-07-30T17:15:11Z First variations of the best Sobolev trace constant with respect to the domain Rossi, Julio Daniel Nonlinear boundary conditions Sobolev trace embedding In this paper we study the best constant of the Sobolev trace embedding H 1 (Ω) → L 2 (∂Ω), where Ω is a bounded smooth domain in ℝ N . We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume. © Canadian Mathematical Society 2008. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00084395_v51_n1_p140_Rossi http://hdl.handle.net/20.500.12110/paper_00084395_v51_n1_p140_Rossi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Nonlinear boundary conditions
Sobolev trace embedding
spellingShingle Nonlinear boundary conditions
Sobolev trace embedding
Rossi, Julio Daniel
First variations of the best Sobolev trace constant with respect to the domain
topic_facet Nonlinear boundary conditions
Sobolev trace embedding
description In this paper we study the best constant of the Sobolev trace embedding H 1 (Ω) → L 2 (∂Ω), where Ω is a bounded smooth domain in ℝ N . We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume. © Canadian Mathematical Society 2008.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title First variations of the best Sobolev trace constant with respect to the domain
title_short First variations of the best Sobolev trace constant with respect to the domain
title_full First variations of the best Sobolev trace constant with respect to the domain
title_fullStr First variations of the best Sobolev trace constant with respect to the domain
title_full_unstemmed First variations of the best Sobolev trace constant with respect to the domain
title_sort first variations of the best sobolev trace constant with respect to the domain
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00084395_v51_n1_p140_Rossi
http://hdl.handle.net/20.500.12110/paper_00084395_v51_n1_p140_Rossi
work_keys_str_mv AT rossijuliodaniel firstvariationsofthebestsobolevtraceconstantwithrespecttothedomain
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