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, Università di Padova, 7 Via Belzoni, 35131 Padova, Italy

maricond@math.unipd.it

Giulia Treu

Dipartimento di Matematica Pura e Applicata, Università 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. https://doi.org/10.68381/jca12014

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press.