On inverse problems for the multidimensional relativistic Newton equation at fixed energy

TL;DR

This paper investigates inverse scattering and boundary value problems for the multidimensional relativistic Newton equation at fixed energy, establishing uniqueness results for the reconstruction of the external potential.

Contribution

It provides new uniqueness theorems for inverse problems related to the relativistic Newton equation with an external potential at fixed energy.

Findings

Proved uniqueness theorems for inverse scattering at fixed energy.

Established conditions for reconstructing the potential V.

Extended known results to the relativistic setting.

Abstract

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results, we obtain, in particular, theorems of uniqueness.