The role of intrinsic distances in the relaxation of $L^{\infty }$-functionals

Maria Stella Gelli, Francesca Prinari

We consider a supremal functional of the form $$F(u)={\mathrm{esssup}}_{x\in \Omega }f(x,Du(x))$$ where $\Omega \subseteq {\mathbf{R}}^N$ is a regular bounded open set, $u\in W^{1,\inft…