Uniqueness of integrable solutions to first order systems with   integrable tensor-coefficients and applications to elasticity
  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'. 
Johannes Lankeit, Patrizio Neff, Dirk Pauly
math.AP