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

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

2010-03-11

arxiv.org/abs/1003.2305v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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