Lipschitz stability of an inverse boundary value problem for a Schrödinger type equation

Elena Beretta, Maarten V. de Hoop, Lingyun Qiu

Published 2012-03-07, updated 2012-11-28Version 2

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger 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.