{
  "id": "1009.3115",
  "version": "v1",
  "published": "2010-09-16T08:36:54.000Z",
  "updated": "2010-09-16T08:36:54.000Z",
  "title": "Existence of translating solutions to the flow by powers of mean curvature on unbounded domains",
  "authors": [
    "Huai-Yu Jian",
    "Hong-Jie Ju"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain. This problem comes from the study of mean curvature flow and its generalization, the flow by powers of mean curvature. Our approach is a modified version of the classical Perron method, where the solutions to the minimal surface equation are used as sub-solutions and a family auxiliary functions are constructed as super-solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-16T08:36:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "52C44"
    ],
    "keywords": [
      "unbounded domains",
      "translating solutions",
      "minimal surface equation",
      "quasi-linear elliptic equations",
      "mean curvature flow"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2011.01.014",
      "journal": "Journal of Differential Equations",
      "year": 2011,
      "volume": 250,
      "number": 10,
      "pages": 3967
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JDE...250.3967J"
    }
  }
}