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Abstract:

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.

Registro:

Documento: Artículo
Título:The best sobolev trace constant in periodic media for critical and subcritical exponents
Autor:Bonder, J.F.; Orive, R.; Rossi, J.D.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Buenos Aires, Argentina
Departamento de Matemáticas, Universidad Autonoma de Madrid, Crta. Colmenar Viejo km. 15, 28049 Madrid, Spain
Año:2009
Volumen:51
Número:3
Página de inicio:619
Página de fin:630
DOI: http://dx.doi.org/10.1017/S0017089509990048
Título revista:Glasgow Mathematical Journal
Título revista abreviado:Glasgow. Math. J.
ISSN:00170895
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00170895_v51_n3_p619_Bonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v51_n3_p619_Bonder

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Citas:

---------- APA ----------
Bonder, J.F., Orive, R. & Rossi, J.D. (2009) . The best sobolev trace constant in periodic media for critical and subcritical exponents. Glasgow Mathematical Journal, 51(3), 619-630.
http://dx.doi.org/10.1017/S0017089509990048
---------- CHICAGO ----------
Bonder, J.F., Orive, R., Rossi, J.D. "The best sobolev trace constant in periodic media for critical and subcritical exponents" . Glasgow Mathematical Journal 51, no. 3 (2009) : 619-630.
http://dx.doi.org/10.1017/S0017089509990048
---------- MLA ----------
Bonder, J.F., Orive, R., Rossi, J.D. "The best sobolev trace constant in periodic media for critical and subcritical exponents" . Glasgow Mathematical Journal, vol. 51, no. 3, 2009, pp. 619-630.
http://dx.doi.org/10.1017/S0017089509990048
---------- VANCOUVER ----------
Bonder, J.F., Orive, R., Rossi, J.D. The best sobolev trace constant in periodic media for critical and subcritical exponents. Glasgow. Math. J. 2009;51(3):619-630.
http://dx.doi.org/10.1017/S0017089509990048