{
  "id": "1906.06190",
  "version": "v1",
  "published": "2019-06-14T13:11:09.000Z",
  "updated": "2019-06-14T13:11:09.000Z",
  "title": "$H^{s,p}$ regularity theory for a class of nonlocal elliptic equations",
  "authors": [
    "Simon Nowak"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the regularity of weak solutions to a class of nonlocal elliptic equations in Bessel potential spaces $H^{s,p}$ under very mild assumptions on the data. Our main results can be seen as an extension of the well-known $W^{1,p}$ regularity theory for local second-order elliptic equations in divergence form with BMO coefficients to the nonlocal setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T13:11:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R09",
      "35B65",
      "35D30",
      "46E35",
      "47G20"
    ],
    "keywords": [
      "nonlocal elliptic equations",
      "regularity theory",
      "local second-order elliptic equations",
      "bessel potential spaces",
      "mild assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}