{
  "id": "1402.4276",
  "version": "v1",
  "published": "2014-02-18T10:31:26.000Z",
  "updated": "2014-02-18T10:31:26.000Z",
  "title": "Some results of the Lipschitz constant of 1-Field on $\\mathbb{R}^n$",
  "authors": [
    "Erwan Y. Le Gruyer",
    "Thanh Viet Phan"
  ],
  "comment": "E.L.G. and T.V.P. are partially supported by the ANR (Agence Nationale de la Recherche) through HJnet projet ANR-12-BS01-0008-01",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the relations between the Lipschitz constant of $1$-field and the Lipschitz constant of the gradient canonically associated with this $1$-field. Moreover, we produce two explicit formulas that make up Minimal Lipschitz extensions for $1$-field. As consequence of the previous results, for the problem of minimal extension by continuous functions from $\\mathbb{R}^m$ to $\\mathbb{R}^n$, we also produce analogous explicit formulas to those of Bauschke and Wang. Finally, we show that Wells's extensions of $1$-field are absolutely minimal Lipschitz extension when the domain of $1$-field to expand is finite. We provide a counter-example showing that this result is false in general.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-18T10:31:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C20",
      "58C25",
      "46T20"
    ],
    "keywords": [
      "lipschitz constant",
      "absolutely minimal lipschitz extension",
      "produce analogous explicit formulas",
      "minimal extension",
      "wellss extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4276L"
    }
  }
}