Weighted generalized Korn inequality on John domains

TL;DR

This paper proves a weighted generalized Korn inequality on John domains, extending classical results by replacing the symmetric part with the trace-free part in weighted Sobolev spaces.

Contribution

It establishes the validity of a weighted generalized Korn inequality on John domains, incorporating weights based on boundary distance, which was not previously known.

Findings

Korn inequality holds on John domains with weights

Trace-free part replaces symmetric part in inequality

Applicable to weighted Sobolev spaces with boundary distance weights

Abstract

The goal of this work is to show that the generalized Korn inequality that replaces the symmetric part of the differential matrix in the classical Korn inequality by its trace-free part is valid over John domains and weighted Sobolev spaces. The weights considered are nonnegative powers of the distance to the boundary.