Fractional Korn's inequality on subsets of the Euclidean space

TL;DR

This paper presents a simplified proof of the fractional Korn's inequality for subsets of Euclidean space and introduces a framework to derive Korn's inequality from Hardy-type inequalities.

Contribution

The authors provide a new, more straightforward proof of fractional Korn's inequality and establish a framework linking it to Hardy-type inequalities.

Findings

Simplified proof of fractional Korn's inequality

Framework connecting Korn's and Hardy-type inequalities

Applicability to subsets of Euclidean space

Abstract

We give a new, simpler proof of the fractional Korn's inequality for subsets of $\mathbb{R}^d$. We also show a framework for obtaining Korn's inequality directly from the appropriate Hardy-type inequality.