{
  "id": "1604.04060",
  "version": "v1",
  "published": "2016-04-14T07:39:34.000Z",
  "updated": "2016-04-14T07:39:34.000Z",
  "title": "Some regularity properties of viscosity solution defined by Hopf formula",
  "authors": [
    "Nguyen Hoang"
  ],
  "comment": "18 pages. arXiv admin note: text overlap with arXiv:1208.3288, arXiv:1309.2547",
  "categories": [
    "math.AP"
  ],
  "abstract": "Some properties of characteristic curves in connection with viscosity solution of Hamilton-Jacobi equations $(H,\\sigma)$ defined by Hopf formula $u(t,x)=\\max_{q\\in\\R^n}\\{ \\langle x,q\\rangle -\\sigma^*(q)-tH(q)\\}$ are studied. We are concerned with the points where the solution $u(t,x)$ is differentiable, and the strip of the form $\\mathcal R=(0,t_0)\\times \\R^n$ of the domain $\\Omega$ where $u(t,x)$ is of class $C^1(\\mathcal R).$ Moreover, we investigate the propagation of singularities in forward of this solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-14T07:39:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solution",
      "hopf formula",
      "regularity properties",
      "characteristic curves",
      "hamilton-jacobi equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404060H"
    }
  }
}