JournalsaihpcVol. 6pp. 185–209

Variational Problems with Lipschitzian Minimizers

  • F.H. Clarke

    Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succursale A, Montréal, Canada H3C 3J7

  • P.D. Loewen

    Deparartment of Mathematics, University of British Columbia, Vancouver, Canada V6T 1Y4
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Abstract

We review the authors’ intermediate existence theory for the basic problem in the calculus of variation [5]. Then we show that the extremal growth condition (EGC), under which [5] asserts the existence and Lipschitzian regularity of solutions to the basic problem, is actually implied by various growth conditions used to prove Lipschitzian regularity in the past. Our results unify and extend the class of problems known to have Lipschitzian solutions.

Cite this article

F.H. Clarke, P.D. Loewen, Variational Problems with Lipschitzian Minimizers. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), pp. 185–209

DOI 10.1016/S0294-1449(17)30021-5