Existence of Minimizers for Non-Level Convex Supremal Functionals
Abstract
The paper is devoted to determine necessary and sufficient conditions for existence of solutions to the problem inf ess supx ∈ f(∇ u(x)): u ∈ u0 + W1,∞0() 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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