A free boundary problem for the p (x)-Laplacian

We consider the optimization problem of minimizing ∫ Ω frac(1, p (x)) | ∇ u | p (x) + λ (x) χ {u > 0} d x in the class of functions W 1, p ({dot operator}) (Ω) with u - φ 0 ∈ W 0 1, p ({dot operator}) (Ω), for a given φ 0 ≥ 0 and bounded. W 1, p ({dot operator}) (Ω) is the class of weakly dif...

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Autores principales: Bonder, J.F., Martínez, S., Wolanski, N.
Formato: JOUR
Materias:
Free boundaries
Minimization
Variable exponent spaces
Differentiable functions
Free boundary
Free-boundary problems
Lipschitz continuous
Optimization problems
P (x)-Laplacian
Regular surfaces
Optimization
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p1078_Bonder
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0362546X_v72_n2_p1078_Bonder
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spelling todo:paper_0362546X_v72_n2_p1078_Bonder2023-10-03T15:27:22Z A free boundary problem for the p (x)-Laplacian Bonder, J.F. Martínez, S. Wolanski, N. Free boundaries Minimization Variable exponent spaces Differentiable functions Free boundary Free-boundary problems Lipschitz continuous Optimization problems P (x)-Laplacian Regular surfaces Optimization We consider the optimization problem of minimizing ∫ Ω frac(1, p (x)) | ∇ u | p (x) + λ (x) χ {u > 0} d x in the class of functions W 1, p ({dot operator}) (Ω) with u - φ 0 ∈ W 0 1, p ({dot operator}) (Ω), for a given φ 0 ≥ 0 and bounded. W 1, p ({dot operator}) (Ω) is the class of weakly differentiable functions with ∫ Ω | ∇ u | p (x) d x < ∞. We prove that every solution u is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, Ω ∩ ∂ {u > 0}, is a regular surface. © 2009 Elsevier Ltd. All rights reserved. Fil:Martínez, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Wolanski, N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p1078_Bonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Free boundaries
Minimization
Variable exponent spaces
Differentiable functions
Free boundary
Free-boundary problems
Lipschitz continuous
Optimization problems
P (x)-Laplacian
Regular surfaces
Optimization
spellingShingle Free boundaries
Minimization
Variable exponent spaces
Differentiable functions
Free boundary
Free-boundary problems
Lipschitz continuous
Optimization problems
P (x)-Laplacian
Regular surfaces
Optimization
Bonder, J.F.
Martínez, S.
Wolanski, N.
A free boundary problem for the p (x)-Laplacian
topic_facet Free boundaries
Minimization
Variable exponent spaces
Differentiable functions
Free boundary
Free-boundary problems
Lipschitz continuous
Optimization problems
P (x)-Laplacian
Regular surfaces
Optimization
description We consider the optimization problem of minimizing ∫ Ω frac(1, p (x)) | ∇ u | p (x) + λ (x) χ {u > 0} d x in the class of functions W 1, p ({dot operator}) (Ω) with u - φ 0 ∈ W 0 1, p ({dot operator}) (Ω), for a given φ 0 ≥ 0 and bounded. W 1, p ({dot operator}) (Ω) is the class of weakly differentiable functions with ∫ Ω | ∇ u | p (x) d x < ∞. We prove that every solution u is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, Ω ∩ ∂ {u > 0}, is a regular surface. © 2009 Elsevier Ltd. All rights reserved.
format JOUR
author Bonder, J.F.
Martínez, S.
Wolanski, N.
author_facet Bonder, J.F.
Martínez, S.
Wolanski, N.
author_sort Bonder, J.F.
title A free boundary problem for the p (x)-Laplacian
title_short A free boundary problem for the p (x)-Laplacian
title_full A free boundary problem for the p (x)-Laplacian
title_fullStr A free boundary problem for the p (x)-Laplacian
title_full_unstemmed A free boundary problem for the p (x)-Laplacian
title_sort free boundary problem for the p (x)-laplacian
url http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p1078_Bonder
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AT wolanskin afreeboundaryproblemforthepxlaplacian
AT bonderjf freeboundaryproblemforthepxlaplacian
AT martinezs freeboundaryproblemforthepxlaplacian
AT wolanskin freeboundaryproblemforthepxlaplacian
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