Existence and Lipschitz regularity for minima

We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional I(u) = integral (Omega) L(x, u, delu) dx on (u) over bar + W-0(1,q)(Omega) (1 less than or equal to q less than or equal to +infinity) for a class of integrands L(x, z, p) = f(p) + g(x, z) that are convex in (z, p) and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on L.