{
  "id": "0908.3057",
  "version": "v1",
  "published": "2009-08-21T06:19:26.000Z",
  "updated": "2009-08-21T06:19:26.000Z",
  "title": "Existence and Regularity For The Generalized Mean Curvature Flow Equations",
  "authors": [
    "RongLi Huang",
    "JiGuang Bao"
  ],
  "comment": "13pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Dirichlet problem of the degenerate elliptic equation $$ -|\\nabla v|(\\mathrm{div}(\\frac{\\nabla v}{|\\nabla v|})+\\nu)=0 $$ is solvable in viscosity sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-21T06:19:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K65"
    ],
    "keywords": [
      "generalized mean curvature flow equations",
      "regularity",
      "degenerate elliptic equation",
      "approximation method",
      "viscosity solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.3057H"
    }
  }
}