An inverse obstacle problem for the magnetic Schr\"odinger equation

TL;DR

This paper investigates the inverse obstacle problem for the magnetic Schrödinger equation, establishing stability inequalities for reconstructing boundary functions from boundary measurements, with Lipschitzian and logarithmic stability results.

Contribution

It provides new stability estimates for the inverse obstacle problem in the magnetic Schrödinger context, including local Lipschitzian and global logarithmic stability.

Findings

Lipschitzian stability locally in time

Logarithmic stability globally in time

Reconstruction of boundary functions from boundary measurements

Abstract

We establish stability inequalities of an inverse obstacle problem for the magnetic Schr\"odinger equation. We mainly study the problem of reconstructing an unknown function defined on the obstacle boundary from two measurements performed on the boundary of a domain surrounding the obstacle. We show for the inverse problem a Lipschitzian stability locally in time and a logarithmic stability globally in time.