Uniqueness of continuation for semilinear elliptic equations

TL;DR

This paper extends the understanding of the uniqueness of continuation for semilinear elliptic equations, providing new stability estimates and establishing strong and measure-based uniqueness results through linearization techniques.

Contribution

It generalizes existing linear results to semilinear cases and introduces novel stability and uniqueness theorems using linearization methods.

Findings

New stability estimate in the linear case

Strong uniqueness of continuation established

Uniqueness from a set of positive measure proven

Abstract

We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product we obtain a new stability estimate in the linear case. We also show the so-called strong uniqueness of continuation and the uniqueness of continuation from a set of positive measure. These results are derived by using a linearization procedure.