{
  "id": "2106.01546",
  "version": "v1",
  "published": "2021-06-03T02:03:08.000Z",
  "updated": "2021-06-03T02:03:08.000Z",
  "title": "Global propagation of singularities for discounted Hamilton-Jacobi equations",
  "authors": [
    "Chen cui",
    "Jiahui Hong",
    "Zhao Kai"
  ],
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "The main purpose of this paper is to study the global propagation of singularities of viscosity solution to discounted Hamilton-Jacobi equation \\begin{equation}\\label{eq:discount 1}\\tag{HJ$_\\lambda$} \\lambda v(x)+H( x, Dv(x) )=0 , \\quad x\\in \\mathbb{R}^n. \\end{equation} We reduce the problem for equation \\eqref{eq:discount 1} into that for a time-dependent evolutionary Hamilton-Jacobi equation. We proved that the singularities of the viscosity solution of \\eqref{eq:discount 1} propagate along locally Lipschitz singular characteristics which can extend to $+\\infty$. We also obtained the homotopy equivalence between the singular set and the complement of associated the Aubry set with respect to the viscosity solution of equation \\eqref{eq:discount 1}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-03T02:03:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discounted hamilton-jacobi equation",
      "global propagation",
      "singularities",
      "viscosity solution",
      "time-dependent evolutionary hamilton-jacobi equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}