Optimal boundary holes for the Sobolev trace constant

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω of given boundary measure.We prove existence of extremals for this problem, and analyze some particular cases where informati...

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Autores principales: Del Pezzo, Leandro M., Fernandez Bonder, Julian
Publicado: 2011
Materias:
P-Laplace operator
Shape optimization
Steklov eigenvalues
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v251_n8_p2327_DelPezzo
http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_DelPezzo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00220396_v251_n8_p2327_DelPezzo
record_format dspace
spelling paper:paper_00220396_v251_n8_p2327_DelPezzo2023-06-08T14:45:11Z Optimal boundary holes for the Sobolev trace constant Del Pezzo, Leandro M. Fernandez Bonder, Julian P-Laplace operator Shape optimization Steklov eigenvalues In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω 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. © 2011 Elsevier Inc. Fil:Del Pezzo, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v251_n8_p2327_DelPezzo http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_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 P-Laplace operator
Shape optimization
Steklov eigenvalues
spellingShingle P-Laplace operator
Shape optimization
Steklov eigenvalues
Del Pezzo, Leandro M.
Fernandez Bonder, Julian
Optimal boundary holes for the Sobolev trace constant
topic_facet P-Laplace operator
Shape optimization
Steklov eigenvalues
description In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ∥u∥W1,p(ω)p/∥u∥Lq(∂ω)p among functions that vanish in a set contained on the boundary ∂ ω 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. © 2011 Elsevier Inc.
author Del Pezzo, Leandro M.
Fernandez Bonder, Julian
author_facet Del Pezzo, Leandro M.
Fernandez Bonder, Julian
author_sort Del Pezzo, Leandro M.
title Optimal boundary holes for the Sobolev trace constant
title_short Optimal boundary holes for the Sobolev trace constant
title_full Optimal boundary holes for the Sobolev trace constant
title_fullStr Optimal boundary holes for the Sobolev trace constant
title_full_unstemmed Optimal boundary holes for the Sobolev trace constant
title_sort optimal boundary holes for the sobolev trace constant
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v251_n8_p2327_DelPezzo
http://hdl.handle.net/20.500.12110/paper_00220396_v251_n8_p2327_DelPezzo
work_keys_str_mv AT delpezzoleandrom optimalboundaryholesforthesobolevtraceconstant
AT fernandezbonderjulian optimalboundaryholesforthesobolevtraceconstant
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