{
  "id": "2001.01145",
  "version": "v1",
  "published": "2020-01-05T00:38:38.000Z",
  "updated": "2020-01-05T00:38:38.000Z",
  "title": "A free boundary problem with fractional diffusion",
  "authors": [
    "Diego Marcon",
    "Rafayel Teymurazyan"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a free boundary optimization problem for the fractional Laplacian with a volume constraint and a lower bound. We prove existence and optimal H\\\"{o}lder regularity of solutions, as well as derive geometric properties of solutions and of the corresponding exterior free boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-05T00:38:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free boundary problem",
      "fractional diffusion",
      "free boundary optimization problem",
      "corresponding exterior free boundary",
      "volume constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}