On inverse problems in electromagnetic field in classical mechanics at fixed energy

Abstract

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field $(V,B)$, $V\in C^2,$ $B\in C^1$ in classical mechanics. Developing the approach going back to Gerver-Nadirashvili 1983's work on an inverse problem of mechanics, we obtain, in particular, theorems of uniqueness.