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...

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Detalles Bibliográficos
Autores: Fernandez Bonder, Julian, Orive, Rafael, Rossi, Julio Daniel
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
Descripción
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.