An optimization problem with volume constraint for a degenerate quasilinear operator

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We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u...

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Autores principales: Fernández Bonder, J., Martínez, S., Wolanski, N.
Formato: JOUR
Materias:
Free boundaries
Optimal design problems
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00220396_v227_n1_p80_FernandezBonder
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00220396_v227_n1_p80_FernandezBonder2023-10-03T14:25:32Z An optimization problem with volume constraint for a degenerate quasilinear operator Fernández Bonder, J. Martínez, S. Wolanski, N. Free boundaries Optimal design problems We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ { u > 0 } ∩ Ω, is smooth. © 2006 Elsevier Inc. All rights reserved. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 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_00220396_v227_n1_p80_FernandezBonder
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
Optimal design problems
spellingShingle Free boundaries
Optimal design problems
Fernández Bonder, J.
Martínez, S.
Wolanski, N.
An optimization problem with volume constraint for a degenerate quasilinear operator
topic_facet Free boundaries
Optimal design problems
description We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ { u > 0 } ∩ Ω, is smooth. © 2006 Elsevier Inc. All rights reserved.
format JOUR
author Fernández Bonder, J.
Martínez, S.
Wolanski, N.
author_facet Fernández Bonder, J.
Martínez, S.
Wolanski, N.
author_sort Fernández Bonder, J.
title An optimization problem with volume constraint for a degenerate quasilinear operator
title_short An optimization problem with volume constraint for a degenerate quasilinear operator
title_full An optimization problem with volume constraint for a degenerate quasilinear operator
title_fullStr An optimization problem with volume constraint for a degenerate quasilinear operator
title_full_unstemmed An optimization problem with volume constraint for a degenerate quasilinear operator
title_sort optimization problem with volume constraint for a degenerate quasilinear operator
url http://hdl.handle.net/20.500.12110/paper_00220396_v227_n1_p80_FernandezBonder
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AT martinezs anoptimizationproblemwithvolumeconstraintforadegeneratequasilinearoperator
AT wolanskin anoptimizationproblemwithvolumeconstraintforadegeneratequasilinearoperator
AT fernandezbonderj optimizationproblemwithvolumeconstraintforadegeneratequasilinearoperator
AT martinezs optimizationproblemwithvolumeconstraintforadegeneratequasilinearoperator
AT wolanskin optimizationproblemwithvolumeconstraintforadegeneratequasilinearoperator
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