Variational Problems with Lipschitzian Minimizers
Francis H. Clarke, Philip D. Loewen · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 1989
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.