Holder regularity for a classical problem of the calculus of variations

Let Omega subset of R(n) be bounded, open and convex. Let F : R(n) -> R be convex, coercive of order p > 1 and such that the diameters of the projections of the faces of the epigraph of F are uniformly bounded. Then every minimizer of integral(Omega) F(del v(x))dx, v is an element of phi + W(0)(1,1)(Omega, R), is Holder continuous in (Omega) over bar of order p-1/n+p-1 whenever phi is Lipschitz on partial derivative Omega. A similar result for non convex Lagrangians that admit a minimizer follows.