{
  "id": "2006.16631",
  "version": "v1",
  "published": "2020-06-30T09:47:56.000Z",
  "updated": "2020-06-30T09:47:56.000Z",
  "title": "Modulus of Continuity Estimates for Fully Nonlinear Parabolic Equations",
  "authors": [
    "Xiaolong Li"
  ],
  "comment": "comments are welcome, 20 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We prove that the moduli of continuity of viscosity solutions to fully nonlinear parabolic partial differential equations are viscosity subsolutions of suitable parabolic equations of one space variable. As applications, we obtain sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations with bounded initial data, via comparison with one-dimensional solutions. This work extends multiple results of Andrews and Clutterbuck for quasilinear equations to fully nonlinear equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-30T09:47:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35J60",
      "35D40"
    ],
    "keywords": [
      "fully nonlinear parabolic equations",
      "continuity estimates",
      "nonlinear parabolic partial differential equations",
      "fully nonlinear parabolic partial differential",
      "work extends multiple results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}