{
  "id": "1401.6443",
  "version": "v1",
  "published": "2014-01-24T20:19:06.000Z",
  "updated": "2014-01-24T20:19:06.000Z",
  "title": "A one-phase problem for the fractional Laplacian: regularity of flat free boundaries",
  "authors": [
    "Daniela De Silva",
    "Ovidiu Savin",
    "Yannick Sire"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1102.3086",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a one-phase free boundary problem involving a fractional Laplacian $(-\\Delta)^\\alpha$, $0<\\alpha <1,$ and we prove that ``flat free boundaries\" are $C^{1,\\gamma}$. We thus extend the known result for the case $\\alpha=1/2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-24T20:19:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flat free boundaries",
      "fractional laplacian",
      "one-phase problem",
      "one-phase free boundary problem",
      "regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6443D"
    }
  }
}