A comparison principle and the lipschitz continuity for minimizers

Abstract

We give some conditions that ensure the validity of a Comparison Principle for the minimizers of integral functional, without assuming the validity of the Euler-Lagrange equation. We deduce a weak Maximum Principle for (possibly) degenerate elliptic equations and, together with a generalization of the Bounded, Slope Condition, a result on the Lipschitz continuity of minimizers. © Heldermann Verlag.