{
  "id": "1905.11961",
  "version": "v1",
  "published": "2019-05-28T17:32:18.000Z",
  "updated": "2019-05-28T17:32:18.000Z",
  "title": "Almost minimizers for certain fractional variational problems",
  "authors": [
    "Seongmin Jeon",
    "Arshak Petrosyan"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic functions and almost minimizers for the fractional obstacle problem with zero obstacle. We show that for a certain range of parameters, almost minimizers are almost Lipschitz or $C^{1,\\beta}$-regular.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-28T17:32:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N60",
      "35R35"
    ],
    "keywords": [
      "fractional variational problems",
      "minimizers",
      "fractional obstacle problem",
      "fractional harmonic functions",
      "zero obstacle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}