Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 1, Pages 223–238 (Mi smj2191)  

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
References:
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
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 1, Pages 178–190
DOI: https://doi.org/10.1134/S0037446606010198
Bibliographic databases:
Document Type: Article
UDC: 517.954
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Sha11}
\by V.~A.~Sharafutdinov
\paper The geometrical problem of electrical impedance tomography in the disk
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 1
\pages 223--238
\mathnet{http://mi.mathnet.ru/smj2191}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2810264}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 1
\pages 178--190
\crossref{https://doi.org/10.1134/S0037446606010198}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000288172400019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952395749}
Linking options:
  • https://www.mathnet.ru/eng/smj2191
  • https://www.mathnet.ru/eng/smj/v52/i1/p223
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
    Statistics & downloads:
    Abstract page:508
    Full-text PDF :140
    References:86
    First page:16
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024