{
  "id": "1312.1606",
  "version": "v1",
  "published": "2013-12-05T16:25:56.000Z",
  "updated": "2013-12-05T16:25:56.000Z",
  "title": "Weak KAM theorem for Hamilton-Jacobi equations",
  "authors": [
    "Xifeng Su",
    "Jun Yan"
  ],
  "comment": "31 pages",
  "categories": [
    "math.DS",
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this paper, we generalize weak KAM theorem from positive Lagrangian systems to \"proper\" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the properties of the solution semigroup, we prove the convergence of solution semigroup and existence of weak KAM solutions for stationary equations: \\begin{equation*} H(x, u, d_x u)=0. \\end{equation*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-05T16:25:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J50",
      "49L25"
    ],
    "keywords": [
      "generalize weak kam theorem",
      "evolutionary hamilton-jacobi equations",
      "weak kam solutions",
      "stationary equations",
      "implicitly defined solution semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1606S"
    }
  }
}