{
  "id": "2402.02448",
  "version": "v2",
  "published": "2024-02-04T11:19:43.000Z",
  "updated": "2024-02-08T16:32:14.000Z",
  "title": "Fine boundary regularity for the singular fractional p-Laplacian",
  "authors": [
    "Antonio Iannizzotto",
    "Sunra Mosconi"
  ],
  "comment": "47 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the boundary weighted regularity of weak solutions $u$ to a $s$-fractional $p$-Laplacian equation in a bounded smooth domain $\\Omega$ with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case $p\\in(1,2)$ and with $s\\in(0,1)$. We prove that $u/{\\rm d}_\\Omega^s$ has a $\\alpha$-H\\\"older continuous extension to the closure of $\\Omega$, ${\\rm d}_\\Omega(x)$ meaning the distance of $x$ from the complement of $\\Omega$. This result corresponds to that of ref. [28] for the degenerate case $p\\ge 2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-02-08T16:32:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10",
      "35R11",
      "47G20"
    ],
    "keywords": [
      "fine boundary regularity",
      "singular fractional p-laplacian",
      "nonlocal dirichlet type boundary condition",
      "boundary weighted regularity",
      "bounded smooth domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}