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

الأصل · EN

In this paper we prove existence and uniqueness of an entropy solution to the A-obstacle problem, for L¹ data. We also extend the Lewy-Stampacchia inequalities to the general framework of L¹ 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.