{
  "id": "math/0303288",
  "version": "v1",
  "published": "2003-03-24T15:11:00.000Z",
  "updated": "2003-03-24T15:11:00.000Z",
  "title": "Viscosity solutions of Hamilton--Jacobi equations with discontinuous coefficients",
  "authors": [
    "Giuseppe Maria Coclite",
    "Nils Henrik Risebro"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Hamilton--Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results are the existence and well--posedness of a viscosity solution to the Cauchy problem. We define a viscosity solution by treating the discontinuities in the coefficients analogously to ``internal boundaries''. By defining an appropriate penalization function, we prove that viscosity solutions are unique. The existence of viscosity solutions is established by showing that a sequence of front tracking approximations is compact in $L^\\infty$, and that the limits are viscosity solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-24T15:11:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solution",
      "hamilton-jacobi equations",
      "discontinuous coefficients",
      "appropriate penalization function",
      "front tracking approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3288C"
    }
  }
}