{
  "id": "1002.4087",
  "version": "v2",
  "published": "2010-02-22T09:48:55.000Z",
  "updated": "2014-12-16T11:19:57.000Z",
  "title": "SBV regularity for Hamilton-Jacobi equations in $\\mathbb R^n$",
  "authors": [
    "Stefano Bianchini",
    "Camillo De Lellis",
    "Roger Robyr"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \\partial_t u + H(D_{x} u)=0 \\qquad \\textrm{in} \\Omega\\subset \\mathbb R\\times \\mathbb R^{n} . $$ In particular, under the assumption that the Hamiltonian $H\\in C^2(\\mathbb R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\\partial_t u$ belong to the class $SBV_{loc}(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-22T09:48:55.000Z",
      "title": "SBV regularity for Hamilton-Jacobi equations in $\\R^n$",
      "abstract": "In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \\partial_t u + H(D_{x} u)=0 \\qquad \\textrm{in} \\Omega\\subset \\R\\times \\R^{n} . $$ In particular, under the assumption that the Hamiltonian $H\\in C^2(\\R^n)$ is uniformly convex, we prove that $D_{x}u$ and $\\partial_t u$ belong to the class $SBV_{loc}(\\Omega)$.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-16T11:19:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35D40",
      "49Q15",
      "34H05"
    ],
    "keywords": [
      "hamilton-jacobi equations",
      "sbv regularity",
      "viscosity solutions",
      "assumption"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-010-0381-z",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2011,
      "month": "Jun",
      "volume": 200,
      "number": 3,
      "pages": 1003
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011ArRMA.200.1003B"
    }
  }
}