{
  "id": "1910.06009",
  "version": "v1",
  "published": "2019-10-14T09:38:53.000Z",
  "updated": "2019-10-14T09:38:53.000Z",
  "title": "Extendability of functions with partially vanishing trace",
  "authors": [
    "Russell M. Brown",
    "Robert Haller-Dintelmann",
    "Patrick Tolksdorf"
  ],
  "comment": "26 pages, 7 Figures",
  "categories": [
    "math.CA",
    "math.AP",
    "math.FA"
  ],
  "abstract": "Let $\\Omega \\subset \\mathbb{R}^d$ be an open set and $D$ be a closed part of its boundary. Under very mild assumptions on $\\Omega$, we construct a bounded Sobolev extension operator for the Sobolev spaces $\\mathrm{W}^{1 , p}_D (\\Omega)$, $1 \\leq p \\leq \\infty$, containing all $\\mathrm{W}^{1 , p} (\\Omega)$-functions that vanish in some sense on $D$. In comparison to other constructions of Brewster et. al. and Haller-Dintelmann et. al. the main focus of this work is to generalize the geometric conditions at the boundary dividing $D$ and $\\partial \\Omega \\setminus D$ that ensure the existence of an extension operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-14T09:38:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partially vanishing trace",
      "extendability",
      "bounded sobolev extension operator",
      "open set",
      "geometric conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}