On the A-Obstacle Problem and the Hausdorff Measure of its Free Boundary
Analysis of PDEs
2010-03-12 v1
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-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.
Keywords
Cite
@article{arxiv.1003.2305,
title = {On the A-Obstacle Problem and the Hausdorff Measure of its Free Boundary},
author = {S. Challal and A. Lyaghfouri and J. F. Rodrigues},
journal= {arXiv preprint arXiv:1003.2305},
year = {2010}
}