Calculus of Variations and Geometric Measure Theory

F. Sk

Characterization of fractional Sobolev--Poincaré and (localized) Hardy inequalities

created by sk on 05 Oct 2022
modified on 17 Apr 2023


Accepted Paper

Inserted: 5 oct 2022
Last Updated: 17 apr 2023

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

ArXiv: 2204.06636 PDF


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 $s\in(0,1)$, $p>1$.