An optimization problem with volume constraint in 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...
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| Lenguaje: | Inglés |
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2008
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v340_n2_p1407_Martinez |
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paperaa:paper_0022247X_v340_n2_p1407_Martinez2023-06-12T16:44:09Z An optimization problem with volume constraint in Orlicz spaces J. Math. Anal. Appl. 2008;340(2):1407-1421 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. 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_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) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| 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 |
Artículo Artículo publishedVersion |
| 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 |
| publishDate |
2008 |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v340_n2_p1407_Martinez |
| work_keys_str_mv |
AT martinezs anoptimizationproblemwithvolumeconstraintinorliczspaces AT martinezs optimizationproblemwithvolumeconstraintinorliczspaces |
| _version_ |
1769810219442896896 |