On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem

Abstract

ABSTRACT In this note we reprove the Lipschitz stability for the inverse problem for the Schrödinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schrödinger version of the argument from Kohn and Vogelius [Determining conductivity by boundary measurements. II. Interior results. Comm Pure Appl Math. 1985;38(5):643–667] and presents a slight variant of the strategy considered in Alessandrini et al. [Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data. Asymptotic Anal. 2018;108:115–149] which may prove useful also in the context of more general operators.