{
  "id": "1403.5624",
  "version": "v4",
  "published": "2014-03-22T08:07:58.000Z",
  "updated": "2014-09-17T03:58:57.000Z",
  "title": "Convergence of the Allen-Cahn equation with Neumann boundary conditions",
  "authors": [
    "Masashi Mizuno",
    "Yoshihiro Tonegawa"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-01T06:17:49.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-17T03:58:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "35K20",
      "53C44"
    ],
    "keywords": [
      "neumann boundary conditions",
      "allen-cahn equation",
      "brakkes mean curvature flow",
      "convergence",
      "general initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5624M"
    }
  }
}