Accepted Paper

Inserted: 5 oct 2022
Last Updated: 17 apr 2023

Journal: Journal of Geometric Analysis
Pages: 18
Year: 2023

Abstract:

In this paper, we prove capacitary versions of the fractional Sobolev--Poincar\'e inequalities. We characterize localized variant of the boundary fractional Sobolev--Poincar\'e inequalities through uniform fatness condition of the domain in $\mathbb{R}^n$. Existence type results on the fractional Hardy inequality are established in the supercritical case $sp>n$ for $s\in(0,1)$, $p>1$.

Download:

• hardy.pdf