The Landis conjecture on exponential decay

A. Logunov, E. Malinnikova, N. Nadirashvili, F. Nazarov

Published 2020-07-14Version 1

Consider a solution $u$ to $\Delta u +Vu=0$ on $\mathbb{R}^2$, where $V$ is real-valued, measurable and $|V|\leq 1$. If $|u(x)| \leq \exp(-C |x| \log^{1/2}|x|)$, $|x|>2$, where $C$ is a sufficiently large absolute constant, then $u\equiv 0$.