Let Omega subset of R-N be an open subset, for a positive integer N, and let L subset of C circle times T Omega be a C-infinity -smooth locally integrable subbundle. We give a proof of the following result: If (Omega, L) is nowhere strictly hypoanalytically pseudoconvex (as defined in the paper) then for any sufficiently small domain omega (sic) Omega, and any f C-0(omega) which is continuous up to the boundary such that f is a solution with respect to L on., it holds true that max(z is an element of partial derivative omega) |f(z)| = max(z is an element of(omega) over bar) |f(z)|. We also point out a relation to Levi curvature.