On L 2 Solvability of BVPs for Elliptic Systems

In this article we prove solvability results for L ² boundary value problems of some elliptic systems Lu=0 on the upper half-space ${mathbb{R}} ^{n+1}_{+}, nge1$ , with transversally independent coefficients. We use the first order formalism introduced by Auscher-Axelsson-McIntosh and further developed with a better understanding of the classes of solutions in the subsequent work of Auscher-Axelsson. The interesting fact is that we prove only half of the Rellich boundary inequality without knowing the other half.