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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00018708_v218_n6_p1914_Martinez https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v218_n6_p1914_Martinez_oai |
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I28-R145-paper_00018708_v218_n6_p1914_Martinez_oai2024-08-16 Martínez, S. Wolanski, N. 2008 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00018708_v218_n6_p1914_Martinez info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Adv. Math. 2008;218(6):1914-1971 Free boundaries Minimization Orlicz spaces A minimum problem with free boundary in Orlicz spaces info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v218_n6_p1914_Martinez_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (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 |
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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00018708_v218_n6_p1914_Martinez_oai |
| work_keys_str_mv |
AT martinezs aminimumproblemwithfreeboundaryinorliczspaces AT wolanskin aminimumproblemwithfreeboundaryinorliczspaces AT martinezs minimumproblemwithfreeboundaryinorliczspaces AT wolanskin minimumproblemwithfreeboundaryinorliczspaces |
| _version_ |
1809356941680443392 |