{
  "id": "1806.08048",
  "version": "v1",
  "published": "2018-06-21T02:25:07.000Z",
  "updated": "2018-06-21T02:25:07.000Z",
  "title": "Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian",
  "authors": [
    "Juan Pablo Borthagaray",
    "Ricardo H. Nochetto",
    "Abner J. Salgado"
  ],
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian. The weight is a power of the distance to the boundary. These bounds then serve us as a guide in the design and analysis of an optimal finite element scheme over graded meshes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-21T02:25:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral fractional laplacian",
      "weighted sobolev regularity",
      "obstacle problem",
      "approximation",
      "optimal finite element scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}