Existence of minimizers for nonlevel convex supremal functionals

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Abstract

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 language Unknown 3341-3370 SIAM Journal on Control and Optimization 52 5 https://doi.org/10.1137/13094390X Published - 1 Jan 2014