Lower semicontinuity of L∞ functionals

  • E.N. Barron

    Department of Mathematical & Computer Sciences, Loyola University Chicago, Chicago, IL 60626, USA
  • R.R. Jensen

    Department of Mathematical & Computer Sciences, Loyola University Chicago, Chicago, IL 60626, USA
  • C.Y. Wang

    Department of Mathematical & Computer Sciences, Loyola University Chicago, Chicago, IL 60626, USA; Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA

Abstract

We study the lower semicontinuity properties and existence of a minimizer of the functional

on . We introduce the notions of Morrey quasiconvexity, polyquasiconvexity, and rank-one quasiconvexity, all stemming from the notion of quasiconvexity (= convex level sets) of in the last variable. We also formally derive the Aronsson–Euler equation for such problems.

Résumé

On examine les propriétés de semi-continuité inférieure et l’existence du minimizeur de la fonctionnelle

sur . On introduit les idées du quasi-convexité de Morrey, du polyquasi-convexité, et du quasi-convexité du rang-un, qui suivent tous de l’idée de quasi-convexité ( = les ensembles à niveau convexes) de à la dernière variable. En plus, on en déduit dans les formes l’équation d’Aronsson–Euler pour de tels problèmes.

Cite this article

E.N. Barron, R.R. Jensen, C.Y. Wang, Lower semicontinuity of L∞ functionals. Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), no. 4, pp. 495–517

DOI 10.1016/S0294-1449(01)00070-1