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arXiv · 1308.3307

Existence of Minimizers for Non-Level Convex Supremal Functionals

Ana Margarida Ribeiro·Elvira Zappale
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Abstract

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.

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Ana Margarida Ribeiro, Elvira Zappale. 2013-08-15. Existence of Minimizers for Non-Level Convex Supremal Functionals. https://arxiv.org/abs/1308.3307

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