Stability estimates for recovering the potential by the impedance boundary map

M. I. Isaev; R. G. Novikov

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

Stability estimates for recovering the potential by the impedance boundary map

M. I. Isaev
, R. G. Novikov

Ecole polytechnique
Moscow Institute of Physics and Technology
IEPT RAS

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	23-41
Number of pages	19
Journal	St. Petersburg Mathematical Journal
Volume	25
Issue number	1
DOIs	https://doi.org/10.1090/S1061-0022-2013-01278-7
Publication status	Published - 1 Jan 2013

Keywords

Impedance boundary map
Inverse boundary value problems
Stability estimate

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10.1090/S1061-0022-2013-01278-7

Cite this

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abstract = "The impedance boundary map (or Robin-to-Robin map) is studied for the Schr{\"o}dinger 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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AU - Novikov, R. G.

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N2 - 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.

AB - 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.

KW - Impedance boundary map

KW - Inverse boundary value problems

KW - Stability estimate

UR - https://www.scopus.com/pages/publications/84889663981

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DO - 10.1090/S1061-0022-2013-01278-7

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JF - St. Petersburg Mathematical Journal

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Stability estimates for recovering the potential by the impedance boundary map

Abstract

Keywords

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