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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todo:paper_00018708_v218_n6_p1914_Martinez2023-10-03T13:52:16Z A minimum problem with free boundary in Orlicz spaces 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. JOUR 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 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| 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 |
JOUR |
| 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 |
| 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 |
| _version_ |
1807319004089417728 |