Quantitative uniqueness for Schrodinger operator with regular potentials

TL;DR

This paper establishes a precise upper bound on how quickly solutions to the Schrödinger equation with regular potentials can vanish, using advanced Carleman inequalities on smooth manifolds.

Contribution

It extends existing methods to include magnetic potentials and provides sharp bounds on solution vanishing orders for Schrödinger operators with C^1 potentials.

Findings

Sharp upper bound on vanishing order of solutions

Extension of Carleman inequalities to magnetic potentials

Applicable to Schrödinger equations on smooth manifolds

Abstract

We give a sharp upper bound on the vanishing order of solutions to Schrodinger equation with C^1 electric and magnetic potentials on a compact smooth manifold. Our method is based on quantitative Carleman type inequalities developed by Donnelly and Fefferman. It also extends the first author's previous work to the magnetic potential case.