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

2012/03/07 by Beretta, Elena, de Hoop, Maarten V., Qiu, Lingyun · 1 citation
#35J57 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.1650

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.

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