Lipschitz Stability of an Inverse Boundary Value Problem for a Schrödinger-Type Equation

Elena Beretta, Maarten V. de Hoop, Lingyun Qiu

Abstract: In this paper we study the inverse boundary value problem of determining the potential in the Schrödinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz-type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.