{
  "id": "2206.12537",
  "version": "v1",
  "published": "2022-06-25T02:31:43.000Z",
  "updated": "2022-06-25T02:31:43.000Z",
  "title": "Hamilton-Jacobi equations with monotone nonlinearities on convex cones",
  "authors": [
    "Hong-Bin Chen",
    "Jiaming Xia"
  ],
  "comment": "30 pages; comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-25T02:31:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A02",
      "35D40",
      "35F21"
    ],
    "keywords": [
      "hamilton-jacobi equation",
      "monotone nonlinearities",
      "nonlinearity",
      "viscosity sense",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}