{
  "id": "1912.09153",
  "version": "v1",
  "published": "2019-12-19T12:10:31.000Z",
  "updated": "2019-12-19T12:10:31.000Z",
  "title": "Averaging of Hamilton-Jacobi equations over Hamiltonian flows",
  "authors": [
    "Hitoshi Ishii",
    "Taiga Kumagai"
  ],
  "comment": "27 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the asymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large drift terms, where the drift terms are given by the Hamiltonian vector fields of Hamiltonian $H$. This is an attempt to understand the averaging effect for fully nonlinear degenerate elliptic equations. In this work, we restrict ourselves to the case of Hamilton-Jacobi equations. The second author has already established averaging results for Hamilton-Jacobi equations with convex Hamiltonians ($G$ below) under the classical formulation of the Dirichlet condition. Here we treat the Dirichlet condition in the viscosity sense, and establish an averaging result for Hamilton-Jacobi equations with relatively general Hamiltonian $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-19T12:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B25",
      "35F21",
      "35F30",
      "49L25"
    ],
    "keywords": [
      "hamilton-jacobi equations",
      "hamiltonian flows",
      "dirichlet condition",
      "fully nonlinear degenerate elliptic equations",
      "hamiltonian vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}