Journal of Convex Analysis 12 (2005), No. 1, 197--212
Copyright Heldermann Verlag 2005
A Comparison Principle and the Lipschitz Continuity for Minimizers
Carlo Mariconda
Dipartimento di Matematica Pura e Applicata, Universita di Padova, 7 Via Belzoni, 35131 Padova, Italy
maricond@math.unipd.it
Giulia Treu
Dipartimento di Matematica Pura e Applicata, Universita di Padova, 7 Via Belzoni, 35131 Padova, Italy
treu@math.unipd.it
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.
Keywords: Comparison Principle, Maximum Principle, variational equation, Euler-Lagrange equation, elliptic equation, Bounded Slope Condition, regularity of minimizers.
MSC: 35A15; 35B05 35B50, 35J20, 46B99
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