{
  "id": "1508.07172",
  "version": "v1",
  "published": "2015-08-28T12:00:15.000Z",
  "updated": "2015-08-28T12:00:15.000Z",
  "title": "An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus",
  "authors": [
    "Jianfeng Lu",
    "Felix Otto"
  ],
  "comment": "28 pages, 3 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study an isoperimetric problem the energy of which contains the perimeter of a set, Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as a point charge with charge $Z$. For the variational problem with constrained volume $V$, our main result is that the minimizer does not exist if $V - Z$ is larger than a constant multiple of $\\max(Z^{2/3}, 1)$. The main technical ingredients of our proof are a uniform density lemma and electrostatic screening arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-28T12:00:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isoperimetric problem",
      "coulomb repulsion",
      "background nucleus",
      "attraction",
      "uniform density lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150807172L"
    }
  }
}