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

## TL;DR

This paper discusses techniques for analyzing the quantitative behavior of solutions to second order elliptic PDEs, focusing on propagation of smallness and zero sets of eigenfunctions, with applications in mathematical physics.

## Contribution

It provides an outline of a recent proof on propagation of smallness and explores its connections to eigenfunction zero sets, offering insights into elliptic PDE analysis.

## Key findings

- Proof outline for propagation of smallness
- Connection between smallness propagation and eigenfunction zero sets
- Basic facts about elliptic PDEs in divergence form

## 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.