APDE seminar @UPV/EHU: On the Landis conjecture

In this talk, I will present partial affirmative answer to the Landis conjecture in all dimensions. The conjecture concerns the fastest speed at which a solution of a Schrödinger equation in $\mathbb{R}^N$ can decrease at infinity. Such results are referred as unique continuation at infinity. We provide a sharp decay criterion that ensures when a solution of a nonnegative Schrödinger equation in $\mathbb{R}^N$ with a potential V ≤ 1 is trivial. Our approach relies on the application of Liouville comparison principles and criticality theory.

Based on a joint work with Yehuda Pinchover.