{
  "id": "1309.7499",
  "version": "v1",
  "published": "2013-09-28T20:20:35.000Z",
  "updated": "2013-09-28T20:20:35.000Z",
  "title": "Semilinear equations involving the fractional Laplacian on domains",
  "authors": [
    "Wenxiong Chen",
    "Yanqin Fang",
    "Ray Yang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Applying the method of moving planes in integral forms, we establish radial symmetry for positive solutions to a class of semilinear equations involving the fractional Laplacian in the unit ball and obtain Liouville type theorems concerning the non-existence of positive solutions in the half space. The regularity of solutions are also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-28T20:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R09"
    ],
    "keywords": [
      "fractional laplacian",
      "semilinear equations",
      "positive solutions",
      "establish radial symmetry",
      "unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7499C"
    }
  }
}