{
  "id": "1712.04875",
  "version": "v1",
  "published": "2017-12-13T17:32:50.000Z",
  "updated": "2017-12-13T17:32:50.000Z",
  "title": "On the best constant in {G}affney inequality",
  "authors": [
    "Gyula Csato",
    "Bernard Dacorogna",
    "Swarnendu Sil"
  ],
  "journal": "J. Funct. Anal. 274.2 (2018) pp. 461-503",
  "doi": "10.1016/j.jfa.2017.10.006",
  "categories": [
    "math.FA"
  ],
  "abstract": "We discuss the value of the best constant in Gaffney inequality namely $$ \\lVert \\nabla \\omega \\rVert_{L^{2}}^{2}\\leq C\\left( \\lVert d\\omega\\rVert_{L^{2}}^{2}+\\lVert \\delta\\omega\\rVert_{L^{2}% }^{2}+\\lVert \\omega\\rVert_{L^{2}}^{2}\\right) $$ when either $\\nu\\wedge\\omega=0$ or $\\nu\\,\\lrcorner\\,\\omega=0$ on $\\partial\\Omega.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T17:32:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "best constant",
      "gaffney inequality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}