Quantitative uniqueness for elliptic equations with singular lower order terms

TL;DR

This paper develops quantitative estimates for unique continuation in elliptic equations with singular lower order terms using Carleman inequalities, including three sphere inequalities and propagation of smallness methods.

Contribution

It introduces new quantitative unique continuation results for elliptic equations with singular lower order terms, employing Carleman inequalities and novel propagation techniques.

Findings

Established a three sphere inequality for solutions.

Developed two methods for propagation of smallness.

Provided quantitative estimates of unique continuation.

Abstract

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.