A minimum problem with free boundary in Orlicz spaces

We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) + λ χ{u > 0} d x in the class of functions W1, G (Ω) with u - φ0 ∈ W01, G (Ω), for a given φ0 ≥ 0 and bounded. W1, G (Ω) is the class of weakly differentiable functions with ∫Ω G (| ∇ u |) d x < ∞. The conditions on the...

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Autores principales: Martínez, S., Wolanski, N.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2008
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Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v218_n6_p1914_Martinez
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spelling paperaa:paper_00018708_v218_n6_p1914_Martinez2023-06-12T16:39:28Z A minimum problem with free boundary in Orlicz spaces Adv. Math. 2008;218(6):1914-1971 Martínez, S. Wolanski, N. Free boundaries Minimization Orlicz spaces We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) + λ χ{u > 0} d x in the class of functions W1, G (Ω) with u - φ0 ∈ W01, G (Ω), for a given φ0 ≥ 0 and bounded. W1, G (Ω) is the class of weakly differentiable functions with ∫Ω G (| ∇ u |) d x < ∞. The conditions on the function G allow for a different behavior at 0 and at ∞. 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. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C1, α regularity of their free boundaries near "flat" free boundary points. © 2008 Elsevier Inc. 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. 2008 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00018708_v218_n6_p1914_Martinez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Free boundaries
Minimization
Orlicz spaces
spellingShingle Free boundaries
Minimization
Orlicz spaces
Martínez, S.
Wolanski, N.
A minimum problem with free boundary in Orlicz spaces
topic_facet Free boundaries
Minimization
Orlicz spaces
description We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) + λ χ{u > 0} d x in the class of functions W1, G (Ω) with u - φ0 ∈ W01, G (Ω), for a given φ0 ≥ 0 and bounded. W1, G (Ω) is the class of weakly differentiable functions with ∫Ω G (| ∇ u |) d x < ∞. The conditions on the function G allow for a different behavior at 0 and at ∞. 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. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C1, α regularity of their free boundaries near "flat" free boundary points. © 2008 Elsevier Inc. All rights reserved.
format Artículo
Artículo
publishedVersion
author Martínez, S.
Wolanski, N.
author_facet Martínez, S.
Wolanski, N.
author_sort Martínez, S.
title A minimum problem with free boundary in Orlicz spaces
title_short A minimum problem with free boundary in Orlicz spaces
title_full A minimum problem with free boundary in Orlicz spaces
title_fullStr A minimum problem with free boundary in Orlicz spaces
title_full_unstemmed A minimum problem with free boundary in Orlicz spaces
title_sort minimum problem with free boundary in orlicz spaces
publishDate 2008
url http://hdl.handle.net/20.500.12110/paper_00018708_v218_n6_p1914_Martinez
work_keys_str_mv AT martinezs aminimumproblemwithfreeboundaryinorliczspaces
AT wolanskin aminimumproblemwithfreeboundaryinorliczspaces
AT martinezs minimumproblemwithfreeboundaryinorliczspaces
AT wolanskin minimumproblemwithfreeboundaryinorliczspaces
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