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arXiv · 1203.1650

Lipschitz stability of an inverse boundary value problem for a Schr\"{o}dinger type equation

Elena Beretta·Maarten V. de Hoop·Lingyun Qiu
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Abstract

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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Elena Beretta, Maarten V. de Hoop, Lingyun Qiu. 2012-03-07. Lipschitz stability of an inverse boundary value problem for a Schr\"{o}dinger type equation. https://arxiv.org/abs/1203.1650

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