An optimization problem with volume constraint in Orlicz spaces

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We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) d x in the class of functions W1, G (Ω), with a constraint on the volume of {u > 0}. The conditions on the function G allow for a different behavior at 0 and at ∞. We consider a penalization problem, and we prove that for small...

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Autor principal: Martínez, S.
Formato: JOUR
Materias:
Free boundaries
Optimal design problems
Orlicz spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v340_n2_p1407_Martinez
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0022247X_v340_n2_p1407_Martinez
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spelling todo:paper_0022247X_v340_n2_p1407_Martinez2023-10-03T14:29:12Z An optimization problem with volume constraint in Orlicz spaces Martínez, S. Free boundaries Optimal design problems Orlicz spaces We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) d x in the class of functions W1, G (Ω), with a constraint on the volume of {u > 0}. The conditions on the function G allow for a different behavior at 0 and at ∞. 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. © 2007 Elsevier Inc. All rights reserved. Fil:Martínez, S. 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_0022247X_v340_n2_p1407_Martinez
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
Orlicz spaces
spellingShingle Free boundaries
Optimal design problems
Orlicz spaces
Martínez, S.
An optimization problem with volume constraint in Orlicz spaces
topic_facet Free boundaries
Optimal design problems
Orlicz spaces
description We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) d x in the class of functions W1, G (Ω), with a constraint on the volume of {u > 0}. The conditions on the function G allow for a different behavior at 0 and at ∞. 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. © 2007 Elsevier Inc. All rights reserved.
format JOUR
author Martínez, S.
author_facet Martínez, S.
author_sort Martínez, S.
title An optimization problem with volume constraint in Orlicz spaces
title_short An optimization problem with volume constraint in Orlicz spaces
title_full An optimization problem with volume constraint in Orlicz spaces
title_fullStr An optimization problem with volume constraint in Orlicz spaces
title_full_unstemmed An optimization problem with volume constraint in Orlicz spaces
title_sort optimization problem with volume constraint in orlicz spaces
url http://hdl.handle.net/20.500.12110/paper_0022247X_v340_n2_p1407_Martinez
work_keys_str_mv AT martinezs anoptimizationproblemwithvolumeconstraintinorliczspaces
AT martinezs optimizationproblemwithvolumeconstraintinorliczspaces
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