Solvability of systems of partial differential equations for functions defined on nonconvex sets

We consider systems of partial differential equations with constant coeffic ients of the form (R(D-x, D-y)f = 0, P(D-x)f = g), f, g is an element of C- infinity(Omega), where R (and P) are operators in (n + 1) variables (and in n variables, respectively), g satisfies the compatibility condition R(D-x, D-y,)g = 0 and Omega subset of IRn+1 is open. Let R be elliptic. We show t hat the solvability of such systems for certain nonconvex sets Omega implie s that any localization at infinity of the principle part P-m of P is hyper bolic. In contrast to this result such systems can always be solved on conv ex open sets Omega by the fundamental principle of Ehrenpreis-Palamodov.