{
  "id": "1406.0793",
  "version": "v1",
  "published": "2014-06-03T17:26:59.000Z",
  "updated": "2014-06-03T17:26:59.000Z",
  "title": "Semi-concave singularities and the Hamilton-Jacobi equation",
  "authors": [
    "Patrick Bernard"
  ],
  "journal": "Regular and Chaotic Dynamics 18, 6 (2013) 674-685",
  "doi": "10.1134/S1560354713060075",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the Cauchy problem for the Hamilton-Jacobi equation with a semiconcave initial condition. We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity solution).We also give conditions for an explicit semi-concave function to be a viscosity solution. These conditions generalize the entropy inequality characterizing piecewise smooth solutions of scalar conservation laws in dimension one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-03T17:26:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton-jacobi equation",
      "semi-concave singularities",
      "viscosity solution",
      "semiconcave initial condition",
      "entropy inequality characterizing piecewise smooth"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Regular and Chaotic Dynamics",
      "year": 2013,
      "month": "Nov",
      "volume": 18,
      "number": 6,
      "pages": 674
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013RCD....18..674B"
    }
  }
}