The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary
In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood...
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todo:paper_03082105_v138_n2_p223_Arrieta2023-10-03T15:22:46Z The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary Arrieta, J.M. Rodríguez-Bernal, A. Rossi, J.D. In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood of the boundary. We also analyse symmetry properties of extremals of the latter embedding when Ω is a ball. © 2008 The Royal Society of Edinburgh. 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_03082105_v138_n2_p223_Arrieta |
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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) |
| description |
In this paper we prove that the best constant in the Sobolev trace embedding H1(Ω) → Lq(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H1(Ω) → Lq(ωε, dx/ε), where ω ε = {x ∈ Ω: dist (x, ∂Ω) < ε} is a small neighbourhood of the boundary. We also analyse symmetry properties of extremals of the latter embedding when Ω is a ball. © 2008 The Royal Society of Edinburgh. |
| format |
JOUR |
| author |
Arrieta, J.M. Rodríguez-Bernal, A. Rossi, J.D. |
| spellingShingle |
Arrieta, J.M. Rodríguez-Bernal, A. Rossi, J.D. The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| author_facet |
Arrieta, J.M. Rodríguez-Bernal, A. Rossi, J.D. |
| author_sort |
Arrieta, J.M. |
| title |
The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| title_short |
The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| title_full |
The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| title_fullStr |
The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| title_full_unstemmed |
The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary |
| title_sort |
best sobolev trace constant as limit of the usual sobolev constant for small strips near the boundary |
| url |
http://hdl.handle.net/20.500.12110/paper_03082105_v138_n2_p223_Arrieta |
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