Abstract:Motivated by the direct method in the calculus of variations in L ∞ , our main result identifies the notion of convexity characterizing the weakly * lower semicontinuity of nonlocal supremal functionals: Cartesian level convexity. This new concept coincides with separate level convexity in the one-dimensional setting and is strictly weaker for higher dimensions. We discuss relaxation in the vectorial case, showing that the relaxed functional will not generally maintain the supremal form. Apart from illustratin… Show more
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