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On the penalized obstacle problem in the unit half ball

Abstract : We study the penalized obstacle problem in the unit half ball, i.e. an approximation of the obstacle problem in the unit half ball. The main result states that when the approximation parameter is small enough and when certain level sets are sufficiently close to the hyperplane {x1 = 0}, then these level sets are uniformly C1 regular graphs. As a by-product, we also recover some regularity of the free boundary for the limiting problem, i.e., for the obstacle problem.
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https://hal-enpc.archives-ouvertes.fr/hal-00674618
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Soumis le : lundi 27 février 2012 - 17:06:37
Dernière modification le : lundi 21 mars 2016 - 17:33:39

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  • HAL Id : hal-00674618, version 1

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Erik Lindgren. On the penalized obstacle problem in the unit half ball. Electronic Journal of Differential Equations, Texas State University, Department of Mathematics, 2010, 2010 (9), pp.1-12. ⟨hal-00674618⟩

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