The Landis conjecture on exponential decay
Alexander Logunov, Eugenia Malinnikova, Nikolaï Nadirashvili, Федор Леонидович Назаров · arXiv (Cornell University) · 2020
Consider a solution $u$ to $Δu +Vu=0$ 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 $u\equiv 0$.