Uniqueness of integrable solutions to for integrable tensor coefficients G and applications to elasticity

Let Omega subset of R-N be a Lipschitz domain and I be a relatively open and non-empty subset of its boundary partial derivative Omega. We show that the solution to the linear first-order system del zeta = G zeta, zeta vertical bar Gamma = 0 is unique if G is an element of L1(Omega; R-(NxN)xN) and zeta is an element of W-1,W-1(Omega; R-N). As a consequence, we prove parallel to . parallel to : C-o(infinity)(Omega, Gamma; R-3) -> [0, infinity), u -> parallel to sym(del uP(-1))parallel to L-2(Omega) to be a norm for with Curl , Curl for some p, q > 1 with 1/p + 1/q = 1 as well as det . We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let satisfy sym for some with det . Then, there exist a constant translation vector and a constant skew-symmetric matrix , such that Phi - A Psi + a.