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.
| Original language | English |
|---|---|
| Pages (from-to) | 113-165 |
| Number of pages | 53 |
| Journal | Annali di Matematica Pura ed Applicata |
| Volume | 191 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2012 |
| Externally published | Yes |
Keywords
- A-Laplace operator
- Entropy solution
- Free boundary
- Hausdorff measure
- Lewy-Stampacchia inequalities
- Obstacle problem
- Stability
ASJC Scopus subject areas
- Applied Mathematics