Korn inequality on irregular domains

TL;DR

This paper investigates the weighted Korn inequality on irregular domains like s-John and quasi-hyperbolic boundary domains, demonstrating its sharpness and connection to Poincaré inequalities.

Contribution

It establishes the weighted Korn inequality on specific irregular domains and explores its implications and sharpness, extending previous results in geometric analysis.

Findings

Korn inequality holds on s-John and quasi-hyperbolic domains

Examples demonstrate the sharpness of the inequality

Korn inequalities imply certain Poincaré inequalities

Abstract

In this paper, we study the weighted Korn inequality on some irregular domains, e.g., $s$-John domains and domains satisfying quasi-hyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are presented. Moreover, we show that Korn inequalities imply certain Poincar\'e inequality.