Stability estimates for recovering the potential by the impedance boundary map

Isaev, M.; Novikov, R.

doi:10.1090/S1061-0022-2013-01278-7

Stability estimates for recovering the potential by the impedance boundary map
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by M. I. Isaev and R. G. Novikov
Translated by: the authors

St. Petersburg Math. J. 25 (2014), 23-41

DOI: https://doi.org/10.1090/S1061-0022-2013-01278-7

Published electronically: November 20, 2013

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Abstract:

The impedance boundary map (or Robin-to-Robin map) is studied for the Schrödinger equation in an open bounded domain for fixed energy in the multidimensional case. Global stability estimates are given for recovering the potential by these boundary data and, as a corollary, by the Cauchy data set. In particular, the results include an extension of the Alessandrini identity to the case of the impedance boundary map.

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