{
  "id": "1812.11354",
  "version": "v1",
  "published": "2018-12-29T12:36:36.000Z",
  "updated": "2018-12-29T12:36:36.000Z",
  "title": "Boundary Hölder Regularity for Fully Nonlinear Elliptic Equations on Reifenberg Flat Domains",
  "authors": [
    "Yuanyuan Lian",
    "Kai Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we investigate the boundary H\\\"older regularity for fully nonlinear elliptic equations on Reifenberg flat domains. We will prove that for any $0<\\alpha<1$, there exists $\\delta>0$ such that the solutions are $C^{\\alpha}$ at $x_0\\in \\partial \\Omega$ provided that $\\Omega$ is $(\\delta,R)$-Reifenberg flat at $x_0$ (see Definition 1.1). A similar result for the Poisson equation has been proved by Lemenant and Sire [5], where the Alt-Caffarelli-Friedman's monotonicity formula is used. Besides the generalization to fully nonlinear elliptic equations, our method is simple. In addition, even for the Poisson equation, our result is stronger than that of Lemenant and Sire.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-29T12:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J25",
      "35J60",
      "35D40"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "reifenberg flat domains",
      "boundary hölder regularity",
      "poisson equation",
      "alt-caffarelli-friedmans monotonicity formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}