Optimal $L^p$-approximation of convex sets by convex subsets

Zakaria Fattah, Ilias Ftouhi, Enrique Zuazua

Given a convex set $\Omega$ of ${\mathbb{R}}^n$, we consider the shape optimization problem of finding a convex subset $\omega \subset \Omega$, of a given measure, minimizing the $p$-distance functi…