On the A-obstacle problem and the Hausdorff measure of its free boundary

摘要

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.