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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2008
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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 |
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paper:paper_0362546X_v69_n8_p2479_Saintier2023-06-08T15:35:21Z Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems 1-Laplacian Critical exponents Functions of bounded variations Optimal design problems Shape analysis Sobolev trace embedding Optimal systems Optimization 1-Laplacian Critical exponent Functions of bounded variations Optimal design Shape analysis Sobolev Shape optimization 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. 2008 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 |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
1-Laplacian Critical exponents Functions of bounded variations Optimal design problems Shape analysis Sobolev trace embedding Optimal systems Optimization 1-Laplacian Critical exponent Functions of bounded variations Optimal design Shape analysis Sobolev Shape optimization |
spellingShingle |
1-Laplacian Critical exponents Functions of bounded variations Optimal design problems Shape analysis Sobolev trace embedding Optimal systems Optimization 1-Laplacian Critical exponent Functions of bounded variations Optimal design Shape analysis Sobolev Shape optimization Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
topic_facet |
1-Laplacian Critical exponents Functions of bounded variations Optimal design problems Shape analysis Sobolev trace embedding Optimal systems Optimization 1-Laplacian Critical exponent Functions of bounded variations Optimal design Shape analysis Sobolev Shape optimization |
description |
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. |
title |
Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
title_short |
Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
title_full |
Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
title_fullStr |
Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
title_full_unstemmed |
Estimates of the best Sobolev constant of the embedding of BV (Ω) into L1(∂Ω) and related shape optimization problems |
title_sort |
estimates of the best sobolev constant of the embedding of bv (ω) into l1(∂ω) and related shape optimization problems |
publishDate |
2008 |
url |
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 |
_version_ |
1768543230840799232 |