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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Comparison Principle
  • Maximum Principle
  • variational equation
  • Euler-Lagrange equation
  • elliptic equation
  • Bounded Slope Condition
  • regularity of minimizers

Mathematics Subject Classification

35A15; 35B05 35B50, 35J20, 46B99

Suggested citation

C. Mariconda, G. Treu. “A Comparison Principle and the Lipschitz Continuity for Minimizers.” Journal of Convex Analysis 12 (2005), No. 1, 197–212.

Copyright Banach Press 2005