Traces of functions of bounded deformation

TL;DR

This paper provides a simplified proof of the trace theorem for functions of bounded deformation on Lipschitz domains, establishing the existence of Lebesgue limits on rectifiable sets, which advances understanding in geometric measure theory.

Contribution

It offers a simplified proof of the trace theorem for functions of bounded deformation, clarifying the behavior on rectifiable sets and enhancing theoretical foundations.

Findings

Simplified proof of the trace theorem for bounded deformation functions.

Established existence of Lebesgue limits on rectifiable sets.

Enhanced theoretical understanding of boundary behavior.

Abstract

This paper is devoted to give a simplified proof of the trace theorem for functions of bounded deformation defined on bounded Lipschitz domains of $\mathbb{R}^n$. As a consequence, the existence of one-sided Lebesgue limits on countably $\mathcal{H}^{n-1}$-rectifiable sets is also established.