Existence of minimizers for nonlevel convex supremal functionals

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $\inf\{ {\mathop{\rm ess\: sup }}_{x\in\Omega}\, f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)\}$, 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.Read More:http://epubs.siam.org/doi/abs/10.1137/13094390X
Original languageUnknown
Pages (from-to)3341-3370
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 1 Jan 2014

Cite this