{
  "id": "1201.3381",
  "version": "v2",
  "published": "2012-01-16T21:55:53.000Z",
  "updated": "2017-03-29T19:44:54.000Z",
  "title": "Hyperbolicity of minimizers and regularity of viscosity solutions for random Hamilton-Jacobi equations",
  "authors": [
    "Konstantin Khanin",
    "Ke Zhang"
  ],
  "comment": "Updated version March 2017",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for a family of randomly kicked Hamilton-Jacobi equations, the unique global minimizer is hyperbolic, almost surely. Furthermore, we prove the unique forward and backward viscosity solutions, though in general only Lipshitz, are smooth in a neighbourhood of the global minimizer. Our result generalizes the result of E, Khanin, Mazel and Sinai (\\cite{EKMS00}) to dimension $d\\ge 2$, and extends the result of Iturriaga and Khanin in \\cite{IK03}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-16T21:55:53.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-03-29T19:44:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H20",
      "76F20",
      "34F05",
      "37D25"
    ],
    "keywords": [
      "random hamilton-jacobi equations",
      "hyperbolicity",
      "regularity",
      "unique global minimizer",
      "randomly kicked hamilton-jacobi equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.3381K"
    }
  }
}