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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| Formato: | Artículo publishedVersion |
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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 https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0022247X_v340_n2_p1407_Martinez_oai |
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| Sumario: | 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. |
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