The best Sobolev trace constant in a domain with oscillating boundary
In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillat...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/125781 |
| Acceso en línea: | http://hdl.handle.net/11336/125781 |
| Access Level: | acceso abierto |
| Palabra clave: | HOMOGENIZATION SOBOLEV TRACE EMBEDDING STEKLOV EIGENVALUES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations. |
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