Inverse boundary value problem for Schr\"odinger equation in two dimensions

TL;DR

This paper improves the understanding of inverse boundary value problems for the Schrödinger equation in two dimensions by relaxing regularity conditions on potentials, thus broadening the class of potentials for which uniqueness results hold.

Contribution

It extends previous uniqueness results for the inverse Schrödinger problem by weakening the regularity assumptions on potentials in two dimensions.

Findings

Uniqueness results hold under weaker regularity conditions.

Broader class of potentials can be recovered from boundary data.

Advances the theoretical foundation of inverse boundary value problems.

Abstract

We relax the regularity condition on potentials of the Schr\"odinger equation in uniqueness results on the inverse boundary value problem which were recently proved in [11] and [5].