Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality λ1(Ω) ∥u∥L1(∂Ω) ≤ ∥u∥ W1,1(Ω) that are independent of Ω. These estimates generalize those of [J. Fernandez Bonder, N. Saintier, Estimates for the Sobolev trace constant with critical exponent and applic...

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Detalles Bibliográficos
Publicado: 2008
Materias:
1-Laplacian
Critical exponents
Functions of bounded variations
Optimal design problems
Shape analysis
Sobolev trace embedding
Optimal systems
Optimization
Critical exponent
Optimal design
Sobolev
Shape optimization
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v69_n8_p2479_Saintier
http://hdl.handle.net/20.500.12110/paper_0362546X_v69_n8_p2479_Saintier
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality λ1(Ω) ∥u∥L1(∂Ω) ≤ ∥u∥ W1,1(Ω) that are independent of Ω. These estimates generalize those of [J. Fernandez Bonder, N. Saintier, Estimates for the Sobolev trace constant with critical exponent and applications, Ann. Mat. Pura. Aplicata (in press)] concerning the p-Laplacian to the case p = 1. We apply our results to prove the existence of an extremal for this embedding.We then study an optimal design problem related to λ1, and eventually compute the shape derivative of the functional Ω → λ1(Ω) © 2007 Elsevier Ltd. All rights reserved.

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