A note on the Korn inequality in a n-dimensional context

TL;DR

This paper provides a new proof of the Korn inequality in n-dimensional spaces using classical analysis tools, emphasizing the role of the Poincaré inequality.

Contribution

It introduces a novel proof approach for the Korn inequality in higher dimensions leveraging standard analysis techniques.

Findings

New proof of Korn inequality in n-dimensional spaces

Highlights the importance of Poincaré inequality in the proof

Reinforces the theoretical foundation of Korn inequality

Abstract

In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincar\'{e} inequality plays a fundamental role.