Optimization problem for extremals of the trace inequality in domains with holes
We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is criti...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/16533 |
| Acceso en línea: | http://hdl.handle.net/11336/16533 |
| Access Level: | acceso abierto |
| Palabra clave: | Sobolev Trace Embedding Shape Derivative Steklov Eigenvalues https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this formula, we prove that when Ω is a centered ball, the symmetric hole is critical when we consider deformation that preserve volume but is not optimal for some case. |
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