On the A-obstacle problem and the Hausdorff measure of its free boundary |
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Authors: | S Challal A Lyaghfouri J F Rodrigues |
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Institution: | 1. Fields Institute, 222 College Street, Toronto, M5T 3J1, Canada 2. University of Lisbon/CMAF, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal
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Abstract: | 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?CStampacchia 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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