Optimal boundary holes for the Sobolev trace constant
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases whe...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/14928 |
| Acceso en línea: | http://hdl.handle.net/11336/14928 |
| Access Level: | acceso abierto |
| Palabra clave: | Steklov eigenvalues p-laplace operator shape optimization https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove existence of extremals for this problem, and analyze some particular cases where information about the location of the optimal boundary set can be given. Moreover, we further study the shape derivative of the Sobolev trace constant under regular perturbations of the boundary set. |
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