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arXiv:1003.2305 [math.AP]AbstractReferencesReviewsResources

On the A-Obstacle Problem and the Hausdorff Measure of its Free Boundary

S. Challal, A. Lyaghfouri, J. F. Rodrigues

Published 2010-03-11Version 1

In this paper we prove existence and uniqueness of an entropy solution to the A-obstacle problem, for L^1 data. We also extend the Lewy-Stampacchia inequalities to the general framework of L^1 data, and show convergence and stability results. We then prove that the free boundary has finite N-1 Hausdorff measure, which completes previous works on this subject by Caffarelli for the Laplace operator and by Lee and Shahgholian for the p-Laplace operator when p>2.

Categories: math.AP
Subjects: 35R35, 35B05, 35J60
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