Calculus of Variations and Geometric Measure Theory
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L. Brasco - E. Cinti

On fractional Hardy inequalities in convex sets

created by brasco on 31 Aug 2017
modified on 07 Sep 2017

[BibTeX]

Preprint

Inserted: 31 aug 2017
Last Updated: 7 sep 2017

Pages: 23
Year: 2017

Abstract:

We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodeckii spaces of order $(s,p)$. The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result holds for every $1<p<\infty$ and $0<s<1$, with a constant which is stable as $s$ goes to $1$.

Keywords: fractional Sobolev spaces, Nonlocal operators, Hardy inequality


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