Carleman estimate for the Schr\"odinger equation and application to magnetic inverse problems

TL;DR

This paper develops a Carleman estimate for the Schrödinger equation with magnetic potential and electrostatic potential, enabling stable reconstruction of these potentials from boundary measurements, with applications to inverse problems.

Contribution

It introduces a new global Carleman estimate for the magnetic Schrödinger equation, facilitating Lipschitz stability in inverse boundary value problems.

Findings

Lipschitz stability for magnetic and electrostatic potentials

Global Carleman estimate for Schrödinger equation

Application to magnetic inverse problems

Abstract

We prove that the stationary magnetic potential vector and the electrostatic potential entering the dynamic magnetic Schr\"odinger equation can be Lipschitz stably retrieved through finitely many local boundary measurements of the solution. The proof is by means of a specific global Carleman estimate for the Schr\"odinger equation, established in the first part of the paper.