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

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

2012-03-07

arxiv.org/abs/1203.1650v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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