{
  "id": "math/0703689",
  "version": "v1",
  "published": "2007-03-23T09:11:28.000Z",
  "updated": "2007-03-23T09:11:28.000Z",
  "title": "Convergence of phase-field approximations to the Gibbs-Thomson law",
  "authors": [
    "M. Röger",
    "Y. Tonegawa"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the convergence of phase-field approximations of the Gibbs-Thomson law. This establishes a relation between the first variation of the Van-der-Waals-Cahn-Hilliard energy and the first variation of the area functional. We allow for folding of diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the multiplicity does not affect the Gibbs-Thomson law and that the mean curvature vanishes where diffuse interfaces have collided. We apply our results to prove the convergence of stationary points of the Cahn-Hilliard equation to constant mean curvature surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta-Kawasaki as a model for micro-phase separation in block-copolymers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-23T09:11:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "35B25",
      "35R35",
      "80A22"
    ],
    "keywords": [
      "gibbs-thomson law",
      "phase-field approximations",
      "convergence",
      "first variation",
      "stationary points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}