{
  "id": "1708.05040",
  "version": "v1",
  "published": "2017-08-16T19:07:03.000Z",
  "updated": "2017-08-16T19:07:03.000Z",
  "title": "On the uniqueness of minimisers of Ginzburg-Landau functionals",
  "authors": [
    "Radu Ignat",
    "Luc Nguyen",
    "Valeriy Slastikov",
    "Arghir Zarnescu"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\\mathbb{R}^n$-valued maps under a suitable convexity assumption on the potential and for $H^{1/2} \\cap L^\\infty$ boundary data that is non-negative in a fixed direction $e\\in \\mathbb{S}^{n-1}$. Furthermore, we show that, when minimisers are not unique, the set of minimisers is generated from any of its elements using appropriate orthogonal transformations of $\\mathbb{R}^n$. We also prove corresponding results for harmonic maps",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-16T19:07:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ginzburg-landau functional",
      "minimisers",
      "uniqueness",
      "appropriate orthogonal transformations",
      "harmonic maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}