The best sobolev trace constant in periodic media for critical and subcritical exponents

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In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and...

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Autores principales: Bonder, J.F., Orive, R., Rossi, J.D.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00170895_v51_n3_p619_Bonder
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00170895_v51_n3_p619_Bonder
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spelling todo:paper_00170895_v51_n3_p619_Bonder2023-10-03T14:14:56Z The best sobolev trace constant in periodic media for critical and subcritical exponents Bonder, J.F. Orive, R. Rossi, J.D. In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aε(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) Lq(∂Ω). © 2009 Glasgow Mathematical Journal Trust. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00170895_v51_n3_p619_Bonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aε(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) Lq(∂Ω). © 2009 Glasgow Mathematical Journal Trust.
format JOUR
author Bonder, J.F.
Orive, R.
Rossi, J.D.
spellingShingle Bonder, J.F.
Orive, R.
Rossi, J.D.
The best sobolev trace constant in periodic media for critical and subcritical exponents
author_facet Bonder, J.F.
Orive, R.
Rossi, J.D.
author_sort Bonder, J.F.
title The best sobolev trace constant in periodic media for critical and subcritical exponents
title_short The best sobolev trace constant in periodic media for critical and subcritical exponents
title_full The best sobolev trace constant in periodic media for critical and subcritical exponents
title_fullStr The best sobolev trace constant in periodic media for critical and subcritical exponents
title_full_unstemmed The best sobolev trace constant in periodic media for critical and subcritical exponents
title_sort best sobolev trace constant in periodic media for critical and subcritical exponents
url http://hdl.handle.net/20.500.12110/paper_00170895_v51_n3_p619_Bonder
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