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

2010/03/11 by S. Challal, Challal, S., Abdeslem Lyaghfouri +3 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1003.2305

Abstract

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.

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