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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder |
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todo:paper_00220396_v198_n1_p129_FernandezBonder2023-10-03T14:25:30Z The behavior of the best Sobolev trace constant and extremals in thin domains Fernández Bonder, J. Martínez, S. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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 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 |
JOUR |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00220396_v198_n1_p129_FernandezBonder |
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| _version_ |
1807315384609538048 |