Calculus of Variations and Geometric Measure Theory

A. M. Ribeiro - E. Zappale

Existence of minimizers for non-level convex supremal functionals

created on 15 Jul 2014


Accepted Paper

Inserted: 15 jul 2014

Journal: SIAM Journal on Control and Optimization
Year: 2014


The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem $\inf \left\{{\rm ess}\sup_{x \in \Omega} f(\nabla u(x)): u \in u_0 +W^{1,\infty}_0(\Omega)\right\}$, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.

Keywords: supremal functionals, differential inclusions, convexity, minimizers.