{
  "id": "1712.03265",
  "version": "v1",
  "published": "2017-12-08T19:37:34.000Z",
  "updated": "2017-12-08T19:37:34.000Z",
  "title": "Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation",
  "authors": [
    "Peng Chen",
    "Renming Song",
    "Longjie Xie",
    "Yingchao Xie"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1, 1}$ open sets by using Duhamel formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require $D$ to be $C^{1,\\theta}$ for some $\\theta\\in (\\alpha/2, 1]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-08T19:37:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet fractional laplacian",
      "heat kernel estimates",
      "gradient perturbation",
      "dirichlet heat kernel",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}