Independent box constraints in a graph-area supremum
= Independent box constraints in a graph-area supremum
{title2=$A_{\mathrm{box}}(u)=|\Omega|+|Du|(\Omega)$}
The independent constraints $|\varphi_0|\leq1$ and $|\varphi|\leq1$ separate the dual <supremum> into $|\Omega|+|Du|(\Omega)$. They do not define square-root graph area. For $|\nabla u|=1$ the box-constrained value is $2|\Omega|$, while the <relaxed graph-area functional> is $\sqrt2|\Omega|$.