{
  "id": "1710.00526",
  "version": "v1",
  "published": "2017-10-02T08:20:28.000Z",
  "updated": "2017-10-02T08:20:28.000Z",
  "title": "Convergence of the Allen-Cahn equation with Neumann boundary condition on non-convex domains",
  "authors": [
    "Takashi Kagaya"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a singular limit problem of the Allen-Cahn equation with the homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable assumptions for initial data. The main result is the convergence of the time parametrized family of the diffused surface energy to Brakke's mean curvature flow with a generalized right angle condition on the boundary of the domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-02T08:20:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "35K20",
      "53C44"
    ],
    "keywords": [
      "allen-cahn equation",
      "non-convex domains",
      "convergence",
      "brakkes mean curvature flow",
      "homogeneous neumann boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}