{
  "id": "2008.05356",
  "version": "v1",
  "published": "2020-08-11T14:59:54.000Z",
  "updated": "2020-08-11T14:59:54.000Z",
  "title": "Higher integrability for nonlinear nonlocal equations with irregular kernel",
  "authors": [
    "Simon Nowak"
  ],
  "comment": "28 pages. arXiv admin note: text overlap with arXiv:1906.06190",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces $H^{s,p}$ under a mild continuity assumption on the kernel. By embedding, this also yields regularity in Sobolev-Slobodeckij spaces $W^{s,p}$. Our approach is based on a characterization of Bessel potential spaces in terms of a certain nonlocal gradient-type operator and a perturbation approach commonly used in the context of local elliptic equations in divergence form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T14:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R09",
      "35B65",
      "35D30",
      "46E35",
      "47G20"
    ],
    "keywords": [
      "nonlinear nonlocal equations",
      "higher integrability",
      "irregular kernel",
      "bessel potential spaces",
      "mild continuity assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}