Testfunctions for elliptic systems and maximum principles

In this paper we are studying projections onto convex sets in R-M in order to introduce testfunctions for elliptic systems. We show that the new testf unctions are suited for quasilinear operators in diagonal form. In a first application we give a geometric description of sets allowed for the values of weak solutions of perturbed elliptic systems in terms of the boundary va lues and the maximal angle between the solution and the perturbation.