{
  "id": "1401.7402",
  "version": "v1",
  "published": "2014-01-29T03:23:53.000Z",
  "updated": "2014-01-29T03:23:53.000Z",
  "title": "A Liouville Theorem for the Fractional Laplacian",
  "authors": [
    "Ran Zhuo",
    "Wenxiong Chen",
    "Xuewei Cui",
    "Zixia Yuan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every $\\alpha$-harmonic function bounded either above or below in all of $R^n$ must be constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-29T03:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35S05",
      "45K05"
    ],
    "keywords": [
      "fractional laplacian",
      "classical liouville theorem",
      "harmonic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7402Z"
    }
  }
}