The behavior of the best Sobolev trace constant and extremals in thin domains

In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighte...

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Detalles Bibliográficos
Autores principales:	Fernandez Bonder, Julian, Martínez, Sandra Rita, Rossi, Julio Daniel
Publicado:	2004
Materias:	Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p129_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00220396_v198_n1_p129_FernandezBonder
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spelling	paper:paper_00220396_v198_n1_p129_FernandezBonder2023-06-08T14:45:08Z The behavior of the best Sobolev trace constant and extremals in thin domains Fernandez Bonder, Julian Martínez, Sandra Rita Rossi, Julio Daniel Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Martínez, S. 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. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p129_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants
spellingShingle	Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants Fernandez Bonder, Julian Martínez, Sandra Rita Rossi, Julio Daniel The behavior of the best Sobolev trace constant and extremals in thin domains
topic_facet	Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants
description	In this paper, we study the asymptotic behavior of the best Sobolev trace constant and extremals for the immersion W1,p(Ω) Lq(∂Ω) in a bounded smooth domain when it is contracted in one direction. We find that the limit problem, when rescaled in a suitable way, is a Sobolev-type immersion in weighted spaces over a projection of Ω, W1,p(P(Ω), α) Lq(P(Ω), β). For the special case p = q, this problem leads to an eigenvalue problem with a nonlinear boundary condition. We also study the convergence of the eigenvalues and eigenvectors in this case. © 2003 Elsevier Inc. All rights reserved.
author	Fernandez Bonder, Julian Martínez, Sandra Rita Rossi, Julio Daniel
author_facet	Fernandez Bonder, Julian Martínez, Sandra Rita Rossi, Julio Daniel
author_sort	Fernandez Bonder, Julian
title	The behavior of the best Sobolev trace constant and extremals in thin domains
title_short	The behavior of the best Sobolev trace constant and extremals in thin domains
title_full	The behavior of the best Sobolev trace constant and extremals in thin domains
title_fullStr	The behavior of the best Sobolev trace constant and extremals in thin domains
title_full_unstemmed	The behavior of the best Sobolev trace constant and extremals in thin domains
title_sort	behavior of the best sobolev trace constant and extremals in thin domains
publishDate	2004
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p129_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
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The behavior of the best Sobolev trace constant and extremals in thin domains

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