Electron. J. Diff. Equ., Vol. 2010(2010), No. 09, pp. 1-12.

On the penalized obstacle problem in the unit half ball

Erik Lindgren

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 $\{x_1=0\}$, then these level sets are uniformly $C^1$ 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.

Submitted September 21, 2009. Published January 16, 2010.
Math Subject Classifications: 35J70, 35J60, 35J85
Key Words: Obstacle problem; elliptic equation; regularity; penalization.

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Erik Lindgren
CERMICS - ENPC, 6 et 8 avenue Blaise Pascal
Cite Descartes Champs sur Marne
77455 Marne la Vallee Cedex 2 France
email: erik.lindgren@cermics.enpc.fr

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