{
  "id": "1812.11357",
  "version": "v1",
  "published": "2018-12-29T12:52:01.000Z",
  "updated": "2018-12-29T12:52:01.000Z",
  "title": "Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations",
  "authors": [
    "Yuanyuan Lian",
    "Kai Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the boundary regularity for viscosity solutions of fully nonlinear elliptic equations. We use a unified, simple method to prove that if the domain $\\Omega$ satisfies the exterior $C^{1,\\mathrm{Dini}}$ condition at $x_0\\in \\partial \\Omega$ (see Definition 1.2), the solution is Lipschitz continuous at $x_0$; if $\\Omega$ satisfies the interior $C^{1,\\mathrm{Dini}}$ condition at $x_0$ (see Definition 1.3), the Hopf lemma holds at $x_0$. The key idea is that the curved boundaries are regarded as perturbations of a hyperplane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-29T12:52:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J25",
      "35J60",
      "35D40"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "boundary lipschitz regularity",
      "hopf lemma holds",
      "boundary regularity",
      "viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}