Existence of Minimizers for Non-Level Convex Supremal Functionals
- Resource Type
- Working Paper
- Authors
- Ribeiro, Ana Margarida; Zappale, Elvira
- Source
- Subject
- Mathematics - Optimization and Control
- Language
The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem ${\rm inf}{{\rm ess sup}_{x \in \Omega} f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)}$ 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.