Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4613667 | Journal of Differential Equations | 2006 | 22 Pages |
Abstract
We consider the optimization problem of minimizing 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.
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Physical Sciences and Engineering
Mathematics
Analysis