{
  "id": "1305.5054",
  "version": "v1",
  "published": "2013-05-22T09:01:16.000Z",
  "updated": "2013-05-22T09:01:16.000Z",
  "title": "A phase field model for the optimization of the Willmore energy in the class of connected surfaces",
  "authors": [
    "Patrick W. Dondl",
    "Luca Mugnai",
    "Matthias Röger"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the surface by a phase field function $u$ taking values close to +1 on the inside of the surface and -1 on its outside. The confinement of the surface is now simply given by the domain of definition of $u$. A diffuse interface approximation for the area functional, as well as for the Willmore energy are well known. We address the topological constraint of connectedness by a nested minimization of two phase fields, the second one being used to identify connected components of the surface. In this article, we provide a proof of Gamma-convergence of our model to the sharp interface limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-22T09:01:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10",
      "74G65"
    ],
    "keywords": [
      "phase field model",
      "optimization",
      "willmore energy connected surfaces",
      "phase field function",
      "diffuse interface approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5054D"
    }
  }
}