A property of Absolute Minimizers in $L^\infty$ Calculus of Variations and of solutions of the Aronsson-Euler equation

Abstract

We discover a new minimality property of the absolute minimizers of supremal functionals, whose variational problems are also known as L ∞ variational problems. In particular for every minimizer v of the quasi-convex functional ess . sup we consider the set suitably defined. If u is an absolute minimizer we give a structure result for A ( u ) and we show that then A ( u ) ⊂ A ( v ) for every minimizer v . Abstract. We discover a new minimality property of the absolute minimizers of supremal functionals (also known as L ∞ Calculus of Variations problems).