LOCAL LIPSCHITZ REGULARITY OF MINIMA FOR A SCALAR PROBLEM OF THE CALCULUS OF VARIATIONS

We consider a functional I(u) = integral(Omega)f(del(x)) dx on u(0) + W(1,1)(Omega). Under the assumption that f is just convex, we prove a new Comparison Principle, we improve and give a short proof of Cellina's Comparison result for a new class of minimizers. We then extend a local Lipschitz regularity result obtained recently by Clarke for a wider class of functions f and boundary data u(0) satisfying a new one-sided Bounded Slope Condition. A relaxation result follows.