We give some conditions that ensure the validity of a Comparison Principle for the Minimizers of integral functionals, 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.
A comparison principle and the Lipschitz continuity for minimizers
MARICONDA, CARLO;TREU, GIULIA
2001
Abstract
We give some conditions that ensure the validity of a Comparison Principle for the Minimizers of integral functionals, 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.
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