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We consider the supremal functional \\[ \\tag{1}\n  \\label{1} \\ \\ \\ \\ \\ \\ \\mathrm{E}_\\infty (u,\\mathcal{O})\\, :=\\, \\| \\mathrm D u \\|_{L^\\infty( \\mathcal{O} )}, \\ \\ \\ \\mathcal{O} \\subseteq \\Omega \\text{ open}, \\] applied to locally Lipschitz mappings $u : \\mathbb R^n \\supseteq \\Omega \\longrightarrow \\mathbb R^N$, where $n,N\\in \\mathbb N$. This is the model functional of Calculus of Variations in $L^\\infty$. The area is developing rapidly, but the vectorial case of $N\\geq 2$ is still poorly understood. 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