{
  "id": "1003.2305",
  "version": "v1",
  "published": "2010-03-11T11:05:43.000Z",
  "updated": "2010-03-11T11:05:43.000Z",
  "title": "On the A-Obstacle Problem and the Hausdorff Measure of its Free Boundary",
  "authors": [
    "S. Challal",
    "A. Lyaghfouri",
    "J. F. Rodrigues"
  ],
  "categories": [
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-11T11:05:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35B05",
      "35J60"
    ],
    "keywords": [
      "hausdorff measure",
      "free boundary",
      "a-obstacle problem",
      "stability results",
      "general framework"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2305C"
    }
  }
}