A Hölder-logarithmic stability estimate for an inverse problem in two dimensions

Abstract

AbstractThe problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient