Calculus of Variations and Geometric Measure Theory

L. Brasco - E. Cinti

On fractional Hardy inequalities in convex sets

created by brasco on 31 Aug 2017
modified on 14 May 2018


Accepted Paper

Inserted: 31 aug 2017
Last Updated: 14 may 2018

Journal: Discrete Contin. Dyn. Syst. Ser. A
Pages: 25
Year: 2017


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