{
  "id": "1404.1629",
  "version": "v2",
  "published": "2014-04-06T22:07:56.000Z",
  "updated": "2014-04-19T17:55:23.000Z",
  "title": "To the theory of viscosity solutions for uniformly elliptic Isaacs equations",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "17 pages, better references, better statements about the dependence of constants on the data",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show how a theorem about solvability in $C^{1,1}$ of special Isaacs equations can be used to obtain existence and uniqueness of viscosity solutions of general uniformly nondegenerate Isaacs equations. We apply it also to establish the $C^{1+\\chi}$ regularity of viscosity solutions and show that finite-difference approximations have an algebraic rate of convergence. The main coefficients of the Isaacs equations are supposed to be in $C^{\\gamma}$ with $\\gamma$ slightly less than $1/2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-19T17:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D40",
      "35J60",
      "49N70",
      "39A14"
    ],
    "keywords": [
      "uniformly elliptic isaacs equations",
      "viscosity solutions",
      "general uniformly nondegenerate isaacs equations",
      "special isaacs equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1629K"
    }
  }
}