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Stability estimates for recovering the potential by the impedance boundary map


Authors: M. I. Isaev and R. G. Novikov
Translated by: the authors
Original publication: Algebra i Analiz, tom 25 (2013), nomer 1.
Journal: St. Petersburg Math. J. 25 (2014), 23-41
MSC (2010): Primary 35J10
DOI: https://doi.org/10.1090/S1061-0022-2013-01278-7
Published electronically: November 20, 2013
MathSciNet review: 3113427
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

M. I. Isaev
Affiliation: Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France – and – Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia
Email: isaev.m.i@gmail.com

R. G. Novikov
Affiliation: Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau, France – and – Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS, Moscow 117997, Russia
Email: novikov@cmap.polytechnique.fr

DOI: https://doi.org/10.1090/S1061-0022-2013-01278-7
Keywords: Impedance boundary map, inverse boundary value problems, stability estimate
Received by editor(s): June 1, 2012
Published electronically: November 20, 2013
Additional Notes: This investigation was supported in part by the Federal Targeted Program no. 14.A18.21.0866 of the RF Ministry of Science and Education. The second author was partially supported by the Russian Federation Government grant no. 2010-220-01-077.
Article copyright: © Copyright 2013 American Mathematical Society

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