Unique determination of a Kato class potential from boundary data

TL;DR

This paper demonstrates that a Kato class potential within a bounded Lipschitz domain in three-dimensional space can be uniquely identified solely from boundary measurements, specifically the Dirichlet-to-Neumann map.

Contribution

It establishes the unique determination of Kato class potentials from boundary data, extending inverse problem results to this class of potentials.

Findings

Kato class potentials are uniquely recoverable from boundary measurements.

The Dirichlet-to-Neumann operator encodes complete information about the potential.

The result applies to Lipschitz domains in three-dimensional space.

Abstract

We prove that a Kato class potential $V$ defined on an open, bounded set in $\mathbb{R}^3$ with Lipschitz boundary is uniquely determined by the Dirichlet-to-Neumann operator associated to the equation $-\Delta u + Vu = 0\,.$