Global stability for the multi-channel Gel'fand-Calder\'on inverse problem in two dimensions

TL;DR

This paper establishes a global logarithmic stability estimate for the multi-channel Gel'fand-Calderón inverse problem in two dimensions, advancing understanding of inverse boundary value problems for matrix-valued potentials.

Contribution

It provides the first global stability estimate for the multi-channel Gel'fand-Calderón inverse problem in 2D, extending previous scalar results to matrix potentials.

Findings

Proves a logarithmic stability estimate for the inverse problem.

Extends inverse boundary value problem results to matrix-valued potentials.

Enhances theoretical understanding of multi-channel inverse problems.

Abstract

We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$.