Uniqueness of integrable solutions to first order systems with integrable tensor-coefficients and applications to elasticity

TL;DR

This paper proves the uniqueness of solutions to certain first order systems with integrable tensor coefficients in Lipschitz domains and applies these results to fundamental inequalities in elasticity theory.

Contribution

It establishes the uniqueness of solutions for specific first order systems and applies this to key results in elasticity, such as Korn's inequality.

Findings

Solutions are unique in Lipschitz domains for the considered systems.

Application of uniqueness results to prove Korn's first inequality.

Derivation of the infinitesimal rigid displacement lemma in curvilinear coordinates.

Abstract

For a Lipschitz domain we show that solutions of certain first order systems are unique. This result is then applied to prove a crucial step for showing Korn's first inequality as well as to prove the 'infinitesimal rigid displacement lemma in curvilinear coordinates'.