English

Existence of Minimizers for Non-Level Convex Supremal Functionals

Optimization and Control 2016-11-26 v1

Abstract

The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem infesssupxΩf(u(x)):uu0+W01,(Ω){\rm inf}{{\rm ess sup}_{x \in \Omega} f(\nabla u(x)): u \in u_0 + W^{1,\infty}_0(\Omega)} when the supremand ff 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 ff are also investigated.

Keywords

Cite

@article{arxiv.1308.3307,
  title  = {Existence of Minimizers for Non-Level Convex Supremal Functionals},
  author = {Ana Margarida Ribeiro and Elvira Zappale},
  journal= {arXiv preprint arXiv:1308.3307},
  year   = {2016}
}
R2 v1 2026-06-22T01:09:40.152Z