{
  "id": "1912.11958",
  "version": "v1",
  "published": "2019-12-27T01:51:50.000Z",
  "updated": "2019-12-27T01:51:50.000Z",
  "title": "Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations",
  "authors": [
    "Yuanyuan Lian",
    "Wenxiu Xu",
    "Kai Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the domain $\\Omega$ satisfies the exterior Reifenberg $C^{1,\\mathrm{Dini}}$ condition at $x_0\\in \\partial \\Omega$ (see Definition 1.3), the solution is Lipschitz continuous at $x_0$; if $\\Omega$ satisfies the interior Reifenberg $C^{1,\\mathrm{Dini}}$ condition at $x_0$ (see Definition 1.4), the Hopf lemma holds at $x_0$. Our paper extends the results under the usual $C^{1,\\mathrm{Dini}}$ condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-27T01:51:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J25",
      "35J60",
      "35D40"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "boundary lipschitz regularity",
      "reifenberg domains",
      "hopf lemma holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}