Closing the gap: Maz'ya-Shaposhnikova and asymptotics of fractional perimeters

Elisa Davoli, Alberto Fanizza, Marco Picerni

We prove a generalization of the Maz'ya-Shaposhnikova formula in the case $p=2$ for functions that may not belong to $L^2({\mathbb{R}}^d)$ and, thus, might not vanish at infinity.…