Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials

TL;DR

This paper investigates inverse boundary value problems for 2D Schrödinger equations with less regular potentials, establishing stability estimates and proving uniqueness for potentials in certain function spaces.

Contribution

It provides the first stability estimate of logarithmic order and proves uniqueness for potentials in $L^p$ spaces with p > 2 in two-dimensional inverse problems.

Findings

Established a conditional stability estimate of logarithmic order.

Proved uniqueness of potentials in $L^p$ class with p > 2.

Extended inverse problem results to less regular potentials.

Abstract

We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness within $L^p$-class of potentials with $p > 2$.