The best Sobolev trace constant in domains with holes for critical or subcritical exponents
In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved fu...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_14461811_v49_n2_p213_Fernandezbonder |
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todo:paper_14461811_v49_n2_p213_Fernandezbonder2023-10-03T16:16:28Z The best Sobolev trace constant in domains with holes for critical or subcritical exponents Fernandezbonder, J. Orive, R. Rossi, J.D. homogenization nonlinear boundary conditions Sobolev trace embedding. In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary. Copyright © Australian Mathematical Society 2007. 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_14461811_v49_n2_p213_Fernandezbonder |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
homogenization nonlinear boundary conditions Sobolev trace embedding. |
| spellingShingle |
homogenization nonlinear boundary conditions Sobolev trace embedding. Fernandezbonder, J. Orive, R. Rossi, J.D. The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| topic_facet |
homogenization nonlinear boundary conditions Sobolev trace embedding. |
| description |
In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with periodically distributed holes inside which we impose that the involved functions vanish. There exists a critical size of the holes for which the limit problem has an extra term. For sizes larger than critical the best trace constant diverges to infinity and for sizes smaller than critical it converges to the best constant in the domain without holes. Also, we study the problem with the holes located on the boundary of the domain. In this case another critical exists and its extra term appears on the boundary. Copyright © Australian Mathematical Society 2007. |
| format |
JOUR |
| author |
Fernandezbonder, J. Orive, R. Rossi, J.D. |
| author_facet |
Fernandezbonder, J. Orive, R. Rossi, J.D. |
| author_sort |
Fernandezbonder, J. |
| title |
The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| title_short |
The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| title_full |
The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| title_fullStr |
The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| title_full_unstemmed |
The best Sobolev trace constant in domains with holes for critical or subcritical exponents |
| title_sort |
best sobolev trace constant in domains with holes for critical or subcritical exponents |
| url |
http://hdl.handle.net/20.500.12110/paper_14461811_v49_n2_p213_Fernandezbonder |
| work_keys_str_mv |
AT fernandezbonderj thebestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents AT oriver thebestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents AT rossijd thebestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents AT fernandezbonderj bestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents AT oriver bestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents AT rossijd bestsobolevtraceconstantindomainswithholesforcriticalorsubcriticalexponents |
| _version_ |
1807316089918455808 |