{
  "id": "2403.17723",
  "version": "v1",
  "published": "2024-03-26T14:11:19.000Z",
  "updated": "2024-03-26T14:11:19.000Z",
  "title": "Regularity for nonlocal equations with local Neumann boundary conditions",
  "authors": [
    "Xavier Ros-Oton",
    "Marvin Weidner"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we establish fine results on the boundary behavior of solutions to nonlocal equations in $C^{k,\\gamma}$ domains which satisfy local Neumann conditions on the boundary. Such solutions typically blow up at the boundary like $v \\asymp d^{s-1}$ and are sometimes called large solutions. In this setup we prove optimal regularity results for the quotients $v/d^{s-1}$, depending on the regularity of the domain and on the data of the problem. The results of this article will be important in a forthcoming work on nonlocal free boundary problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-26T14:11:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47G20",
      "35B65",
      "31B05",
      "35R53",
      "35B44"
    ],
    "keywords": [
      "local neumann boundary conditions",
      "nonlocal equations",
      "nonlocal free boundary problems",
      "satisfy local neumann conditions",
      "optimal regularity results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}