On Poincaré constants related to isoperimetric problems in convex bodies

Dorin Bucur, Ilaria Fragalà

For any convex set $\Omega \subset {\mathbb{R}}^N$, we provide a lower bound for the inverse of the Poincaré constant in $W^{1,1}(\Omega )$: it refines an inequality in terms of the diamete…