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Abstract:

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.

Registro:

Documento: Artículo
Título:The behavior of the best Sobolev trace constant and extremals in thin domains
Autor:Fernández Bonder, J.; Martínez, S.; Rossi, J.D.
Filiación:Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Departamento de Matemática, Universidad Católica, Casilla 306 Correo 22, Santiago, Chile
Palabras clave:Eigenvalue problems; Nonlinear boundary conditions; p-Laplacian; Sobolev trace constants
Año:2004
Volumen:198
Número:1
Página de inicio:129
Página de fin:148
DOI: http://dx.doi.org/10.1016/j.jde.2003.07.011
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v198_n1_p129_FernandezBonder.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v198_n1_p129_FernandezBonder

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Citas:

---------- APA ----------
Fernández Bonder, J., Martínez, S. & Rossi, J.D. (2004) . The behavior of the best Sobolev trace constant and extremals in thin domains. Journal of Differential Equations, 198(1), 129-148.
http://dx.doi.org/10.1016/j.jde.2003.07.011
---------- CHICAGO ----------
Fernández Bonder, J., Martínez, S., Rossi, J.D. "The behavior of the best Sobolev trace constant and extremals in thin domains" . Journal of Differential Equations 198, no. 1 (2004) : 129-148.
http://dx.doi.org/10.1016/j.jde.2003.07.011
---------- MLA ----------
Fernández Bonder, J., Martínez, S., Rossi, J.D. "The behavior of the best Sobolev trace constant and extremals in thin domains" . Journal of Differential Equations, vol. 198, no. 1, 2004, pp. 129-148.
http://dx.doi.org/10.1016/j.jde.2003.07.011
---------- VANCOUVER ----------
Fernández Bonder, J., Martínez, S., Rossi, J.D. The behavior of the best Sobolev trace constant and extremals in thin domains. J. Differ. Equ. 2004;198(1):129-148.
http://dx.doi.org/10.1016/j.jde.2003.07.011