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

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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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Autores principales: Fernández Bonder, J., Martínez, S., Rossi, J.D.
Formato: Artículo publishedVersion
Publicado: 2004
Materias:
Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v198_n1_p129_FernandezBonder_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_00220396_v198_n1_p129_FernandezBonder_oai
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spelling I28-R145-paper_00220396_v198_n1_p129_FernandezBonder_oai2024-08-16 Fernández Bonder, J. Martínez, S. Rossi, J.D. 2004 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Differ. Equ. 2004;198(1):129-148 Eigenvalue problems Nonlinear boundary conditions p-Laplacian Sobolev trace constants The behavior of the best Sobolev trace constant and extremals in thin domains info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v198_n1_p129_FernandezBonder_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
spellingShingle Eigenvalue problems
Nonlinear boundary conditions
p-Laplacian
Sobolev trace constants
Fernández Bonder, J.
Martínez, S.
Rossi, J.D.
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.
format Artículo
Artículo
publishedVersion
author Fernández Bonder, J.
Martínez, S.
Rossi, J.D.
author_facet Fernández Bonder, J.
Martínez, S.
Rossi, J.D.
author_sort Fernández Bonder, J.
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 http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00220396_v198_n1_p129_FernandezBonder_oai
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