An optimization problem with volume constraint for a degenerate quasilinear operator
We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. 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...
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| Autores principales: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00220396_v227_n1_p80_FernandezBonder |
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| Sumario: | We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. 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. © 2006 Elsevier Inc. All rights reserved. |
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