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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 1, Pages 223–238
(Mi smj2191)
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The geometrical problem of electrical impedance tomography in the disk
V. A. Sharafutdinov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
The geometrical problem of electrical impedance tomography consists of recovering a Riemannian metric on a compact manifold with boundary from the Dirichlet-to-Neumann operator (DNoperator) given on the boundary. We present a new elementary proof of the uniqueness theorem: A Riemannian metric on the two-dimensional disk is determined by its DN-operator uniquely up to a conformal equivalence. We also prove an existence theorem that describes all operators on the circle that are DN-operators of Riemannian metrics on the disk.
Keywords:
electrical impedance tomography, Dirichlet-to-Neumann operator, conformal map.
Received: 01.04.2010
Citation:
V. A. Sharafutdinov, “The geometrical problem of electrical impedance tomography in the disk”, Sibirsk. Mat. Zh., 52:1 (2011), 223–238; Siberian Math. J., 52:1 (2011), 178–190
Linking options:
https://www.mathnet.ru/eng/smj2191 https://www.mathnet.ru/eng/smj/v52/i1/p223
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Abstract page: | 508 | Full-text PDF : | 140 | References: | 86 | First page: | 16 |
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