{
  "id": "1508.01400",
  "version": "v1",
  "published": "2015-08-06T13:48:58.000Z",
  "updated": "2015-08-06T13:48:58.000Z",
  "title": "A density problem for Sobolev spaces on planar domains",
  "authors": [
    "Pekka Koskela",
    "Yi Ru-Ya Zhang"
  ],
  "comment": "12 pages with 1 figure",
  "categories": [
    "math.CA",
    "math.AP",
    "math.CV",
    "math.FA"
  ],
  "abstract": "We prove that for a bounded simply connected domain $\\Omega\\subset \\mathbb R^2$, the Sobolev space $W^{1,\\,\\infty}(\\Omega)$ is dense in $W^{1,\\,p}(\\Omega)$ for any $1\\le p<\\infty$. Moreover, we show that if $\\Omega$ is Jordan, then $C^{\\infty}(\\mathbb R^2)$ is dense in $W^{1,\\,p}(\\Omega)$ for $1\\le p<\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-06T13:48:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "sobolev space",
      "planar domains",
      "density problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}