{
  "id": "1609.05681",
  "version": "v1",
  "published": "2016-09-19T12:08:24.000Z",
  "updated": "2016-09-19T12:08:24.000Z",
  "title": "H-distribution via Sobolev spaces",
  "authors": [
    "Jelena Aleksic",
    "Stevan Pilipovic",
    "Ivana Vojnovic"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "H-distributions associated to weakly convergent sequences in Sobolev spaces are determined. It is shown that a weakly convergent sequence $(u_n)$ in $W^{-k,p}( \\R^d)$ has the property that $\\theta u_n$ converges strongly in $W^{-k,p}(\\R^d)$ for every $\\theta\\in\\mathcal S(\\R^d)$ if and only if all H-distributions related to this sequence are equal to zero. Results are applied on a weakly convergent sequence of solutions to a family of linear first order PDEs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-19T12:08:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F25"
    ],
    "keywords": [
      "sobolev spaces",
      "weakly convergent sequence",
      "h-distribution",
      "linear first order pdes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}