{
  "id": "math/0311269",
  "version": "v1",
  "published": "2003-11-16T18:10:06.000Z",
  "updated": "2003-11-16T18:10:06.000Z",
  "title": "Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading",
  "authors": [
    "Michael Malisoff"
  ],
  "comment": "29 pages, 0 figures, accepted for publication in NoDEA Nonlinear Differential Equations and Applications on July 29, 2002",
  "journal": "NoDEA Nonlinear Differential Equations and Applications, Volume 11, Number 1, pp. 95-122, February 2004",
  "doi": "10.1007/s00030-003-1051-8",
  "categories": [
    "math.OC"
  ],
  "abstract": "We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is null on the target. The result applies to problems with the property that all trajectories satisfying a certain integral condition must stay in a bounded set. We allow problems for which the Lagrangian is not uniformly bounded below by positive constants, in which the hypotheses of the known uniqueness results for Hamilton-Jacobi equations are not satisfied. We apply our theorems to eikonal equations from geometric optics, shape-from-shading equations from image processing, and variants of the Fuller Problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-16T18:10:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F20",
      "49L25"
    ],
    "keywords": [
      "hamilton-jacobi equation",
      "optimal control problems",
      "eikonal equations",
      "bounded-from-below solutions",
      "vanishing lagrangians"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11269M"
    }
  }
}