{
  "id": "0910.2721",
  "version": "v2",
  "published": "2009-10-14T20:30:17.000Z",
  "updated": "2010-10-26T08:15:54.000Z",
  "title": "On ground states for the L^2-critical boson star equation",
  "authors": [
    "Rupert L. Frank",
    "Enno Lenzmann"
  ],
  "comment": "Replaced version; see also http://arxiv.org/abs/1009.4042",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider ground state solutions $u \\geq 0$ for the $L^2$-critical boson star equation $$ \\sqrt{-\\Delta} \\, u - \\big (|x|^{-1} \\ast |u|^2 \\big) u = -u \\quad {in $\\R^3$}. $$ We prove analyticity and radial symmetry of $u$. In a previous version of this paper, we also stated uniqueness and nondegeneracy of ground states for the $L^2$-critical boson star equation in $\\R^3$, but the arguments given there contained a gap. However, we refer to our recent preprint \\cite{FraLe} in {\\tt arXiv:1009.4042}, where we prove a general uniqueness and nondegeneracy result for ground states of nonlinear equations with fractional Laplacians in $d=1$ space dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-26T08:15:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical boson star equation",
      "ground state solutions",
      "radial symmetry",
      "space dimension",
      "general uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2721F"
    }
  }
}