Quantitative uniqueness estimates for the general second order elliptic equations

TL;DR

This paper establishes quantitative lower bounds on the decay rates at infinity for solutions to general second order elliptic equations with magnetic and electric potentials, using Carleman and bootstrapping techniques.

Contribution

It provides new decay estimates that depend on the asymptotic behavior of magnetic and electric potentials, extending previous results in elliptic PDEs.

Findings

Lower bounds of decay rates at infinity for solutions

Decay bounds depend on potential asymptotics

Method combines Carleman estimates with bootstrapping

Abstract

In this paper we study quantitative uniqueness estimates of solutions to general second order elliptic equations with magnetic and electric potentials. We derive lower bounds of decay rate at infinity for any nontrivial solution under some general assumptions. The lower bounds depend on asymptotic behaviors of magnetic and electric potentials. The proof is carried out by the Carleman method and the bootstrapping arguments.