A relaxation result in the vectorial setting and $L^p$-approximation for $L^{\infty }$-functionals

Francesca Prinari, Elvira Zappale

We provide relaxation for not lower semicontinuous supremal functionals of the type $W^{1,\infty}(Ω;\mathbb R^d) \ni u \mapsto\supess_{ x \in Ω}f(\nabla u(x))$ in the vectorial cas…