{
  "id": "2002.11994",
  "version": "v1",
  "published": "2020-02-27T09:32:57.000Z",
  "updated": "2020-02-27T09:32:57.000Z",
  "title": "Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies",
  "authors": [
    "Julian Fischer",
    "Tim Laux",
    "Thilo Simon"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen-Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-27T09:32:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature flow",
      "allen-cahn equation",
      "relative entropy",
      "short proof",
      "convergence rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}