Lecture notes on quantitative unique continuation for solutions of second order elliptic equations

Abstract

In these lectures we present some useful techniques to study quantitative properties of solutions of elliptic PDEs. Our aim is to outline a proof of a recent result on propagation of smallness. The ideas are also useful in the study of the zero sets of eigenfunctions of Laplace-Beltrami operator and we discuss the connection. Some basic facts about second order elliptic PDEs in divergent form are collected in the Appendix at the end of the notes.Comment: Lecture notes for Graduate Summer School in Park City (PCMI), July 201