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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Autor principal: Del Pezzo, Leandro M.
Publicado: 2010
Materias:
shape derivative
Sobolev trace embedding
Steklov eigenvalues
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v12_n4_p569_DelPezzo
http://hdl.handle.net/20.500.12110/paper_02191997_v12_n4_p569_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02191997_v12_n4_p569_DelPezzo
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spelling paper:paper_02191997_v12_n4_p569_DelPezzo2023-06-08T15:21:35Z Optimization problem for extremals of the trace inequality in domains with holes Del Pezzo, Leandro M. shape derivative Sobolev trace embedding Steklov eigenvalues 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. © 2010 World Scientific Publishing Company. Fil:Del Pezzo, L.M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v12_n4_p569_DelPezzo http://hdl.handle.net/20.500.12110/paper_02191997_v12_n4_p569_DelPezzo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic shape derivative
Sobolev trace embedding
Steklov eigenvalues
spellingShingle shape derivative
Sobolev trace embedding
Steklov eigenvalues
Del Pezzo, Leandro M.
Optimization problem for extremals of the trace inequality in domains with holes
topic_facet shape derivative
Sobolev trace embedding
Steklov eigenvalues
description 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. © 2010 World Scientific Publishing Company.
author Del Pezzo, Leandro M.
author_facet Del Pezzo, Leandro M.
author_sort Del Pezzo, Leandro M.
title Optimization problem for extremals of the trace inequality in domains with holes
title_short Optimization problem for extremals of the trace inequality in domains with holes
title_full Optimization problem for extremals of the trace inequality in domains with holes
title_fullStr Optimization problem for extremals of the trace inequality in domains with holes
title_full_unstemmed Optimization problem for extremals of the trace inequality in domains with holes
title_sort optimization problem for extremals of the trace inequality in domains with holes
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02191997_v12_n4_p569_DelPezzo
http://hdl.handle.net/20.500.12110/paper_02191997_v12_n4_p569_DelPezzo
work_keys_str_mv AT delpezzoleandrom optimizationproblemforextremalsofthetraceinequalityindomainswithholes
_version_ 1768544548754030592

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