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

被引：0
作者：
S. Challal
A. Lyaghfouri
J. F. Rodrigues
机构：
[1] Fields Institute,
[2] University of Lisbon/CMAF,undefined
来源：
Annali di Matematica Pura ed Applicata | 2012年 / 191卷
关键词：
Obstacle problem; Entropy solution; -Laplace operator; Lewy–Stampacchia inequalities; Stability; Free boundary; Hausdorff measure; 35R35; 35B05; 35J60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：113 / 165
页数：52
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