{
  "id": "1805.06434",
  "version": "v1",
  "published": "2018-05-16T17:23:10.000Z",
  "updated": "2018-05-16T17:23:10.000Z",
  "title": "Fractional Korn and Hardy-type inequalities for vector fields in half space",
  "authors": [
    "Tadele Mengesha"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We prove a fractional Hardy-type inequality for vector fields over the half space based on a modified fractional semi-norm. A priori, the modified semi-norm is not known to be equivalent to the standard fractional semi-norm and in fact gives a smaller norm, in general. As such, the inequality we prove improves the classical fractional Hardy inequality for vector fields. We will use the inequality to establish the equivalence of a space of functions (of interest) defined over the half space with the classical fractional Sobolev spaces, which amounts to proving a fractional version of the classical Korn's inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-16T17:23:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "half space",
      "vector fields",
      "fractional korn",
      "fractional hardy-type inequality",
      "standard fractional semi-norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}