Sharp geometric condition for null-controllability of the heat equation on ${\mathbb{R}}^d$ and consistent estimates on the control cost

Michela Egidi, Ivan Veselic

In this note we study the control problem for the heat equation on ${\mathbb{R}}^d$, $d\ge 1$, with control set $\omega \subset {\mathbb{R}}^d$. We provide a necessary and sufficient conditi…