{
"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"
}
}
}