Two questions of Landis and their applications

Analysis Seminar
Topic:Two questions of Landis and their applications
Speaker:Eugenia Malinnikova
Affiliation:Norwegian University of Science and Technology; von Neumann Fellow, School of Mathematics
Date:Friday, December 14
Time/Room:4:30pm - 5:30pm/Simonyi Hall 101
Video Link:https://video.ias.edu/analysis/2018/1214-EugeniaMalinnikova

We discuss two old questions of Landis concerning behavior of solutions of second order elliptic equations. The first one is on propagation of smallness for solutions from sets of positive measure, we answer this question and as a corollary prove an estimate for eigenfunctions of Laplace operator conjectured by Donnelly and Fefferman. The second question is on the decay rate of solutions of the Schrödinger equation, we give the answer in dimension two. The talk is based on joint work with A. Logunov, N. Nadirashvili, and F. Nazarov.