Calculus of Variations and Geometric Measure Theory

F. Sk

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

created by sk on 05 Oct 2022

[BibTeX]

Submitted Paper

Inserted: 5 oct 2022
Last Updated: 5 oct 2022

Year: 2022

ArXiv: 2204.06636 PDF

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