Standard

Electric impedance tomography problem for surfaces with internal holes *. / Badanin, A V; Belishev, M I; Korikov, D V.

In: Inverse Problems, Vol. 37, No. 10, 105013, 10.2021.

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

Harvard

Badanin, AV, Belishev, MI & Korikov, DV 2021, 'Electric impedance tomography problem for surfaces with internal holes *', Inverse Problems, vol. 37, no. 10, 105013. https://doi.org/10.1088/1361-6420/ac245c

APA

Badanin, A. V., Belishev, M. I., & Korikov, D. V. (2021). Electric impedance tomography problem for surfaces with internal holes *. Inverse Problems, 37(10), [105013]. https://doi.org/10.1088/1361-6420/ac245c

Vancouver

Badanin AV, Belishev MI, Korikov DV. Electric impedance tomography problem for surfaces with internal holes *. Inverse Problems. 2021 Oct;37(10). 105013. https://doi.org/10.1088/1361-6420/ac245c

Author

Badanin, A V ; Belishev, M I ; Korikov, D V. / Electric impedance tomography problem for surfaces with internal holes *. In: Inverse Problems. 2021 ; Vol. 37, No. 10.

BibTeX

@article{c789d8ee940643f3aac68448ad753c8b,
title = "Electric impedance tomography problem for surfaces with internal holes *",
abstract = "Let (M, g) be a smooth compact Riemann surface with the multicomponent boundary . Let u = u f obey Δu = 0 in M, (the grounded holes) and v = v h obey Δv = 0 in M, (the isolated holes). Let and be the corresponding Dirichlet-to-Neumann map. The electric impedance tomography problem is to determine M from or . To solve it, an algebraic variant of the boundary control method is applied. The central role is played by the algebra of functions holomorphic on the manifold obtained by gluing two examples of M along . We show that is determined by (or ) up to isometric isomorphism. A relevant copy (M′, g′, Γ0′) of (M, g, Γ0) is constructed from the Gelfand spectrum of . By construction, this copy turns out to be conformally equivalent to (M, g, Γ0), obeys and provides a solution of the problem.",
keywords = "30F15, 35R30, 46J15, 46J20, algebraic version of boundary control method, determination of Riemann surface from its DN-map, electric impedance tomography of surfaces, MANIFOLDS",
author = "Badanin, {A V} and Belishev, {M I} and Korikov, {D V}",
note = "A V Badanin et al 2021 Inverse Problems 37 105013",
year = "2021",
month = oct,
doi = "10.1088/1361-6420/ac245c",
language = "English",
volume = "37",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "10",

}

RIS

TY - JOUR

T1 - Electric impedance tomography problem for surfaces with internal holes *

AU - Badanin, A V

AU - Belishev, M I

AU - Korikov, D V

N1 - A V Badanin et al 2021 Inverse Problems 37 105013

PY - 2021/10

Y1 - 2021/10

N2 - Let (M, g) be a smooth compact Riemann surface with the multicomponent boundary . Let u = u f obey Δu = 0 in M, (the grounded holes) and v = v h obey Δv = 0 in M, (the isolated holes). Let and be the corresponding Dirichlet-to-Neumann map. The electric impedance tomography problem is to determine M from or . To solve it, an algebraic variant of the boundary control method is applied. The central role is played by the algebra of functions holomorphic on the manifold obtained by gluing two examples of M along . We show that is determined by (or ) up to isometric isomorphism. A relevant copy (M′, g′, Γ0′) of (M, g, Γ0) is constructed from the Gelfand spectrum of . By construction, this copy turns out to be conformally equivalent to (M, g, Γ0), obeys and provides a solution of the problem.

AB - Let (M, g) be a smooth compact Riemann surface with the multicomponent boundary . Let u = u f obey Δu = 0 in M, (the grounded holes) and v = v h obey Δv = 0 in M, (the isolated holes). Let and be the corresponding Dirichlet-to-Neumann map. The electric impedance tomography problem is to determine M from or . To solve it, an algebraic variant of the boundary control method is applied. The central role is played by the algebra of functions holomorphic on the manifold obtained by gluing two examples of M along . We show that is determined by (or ) up to isometric isomorphism. A relevant copy (M′, g′, Γ0′) of (M, g, Γ0) is constructed from the Gelfand spectrum of . By construction, this copy turns out to be conformally equivalent to (M, g, Γ0), obeys and provides a solution of the problem.

KW - 30F15

KW - 35R30

KW - 46J15

KW - 46J20

KW - algebraic version of boundary control method

KW - determination of Riemann surface from its DN-map

KW - electric impedance tomography of surfaces

KW - MANIFOLDS

UR - http://www.scopus.com/inward/record.url?scp=85116909365&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/20fff474-e828-39a8-a45d-59a084158d8a/

U2 - 10.1088/1361-6420/ac245c

DO - 10.1088/1361-6420/ac245c

M3 - Article

VL - 37

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 10

M1 - 105013

ER -

ID: 86584054