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Russian Mathematical Surveys, 2012, Volume 67, Issue 6, Pages 1069–1089
DOI: https://doi.org/10.1070/RM2012v067n06ABEH004818 (Mi rm9501) 		 
This article is cited in 3 scientific papers (total in 4 papers)

Inverse Dirichlet-to-Neumann problem for nodal curves

G. Henkinab, V. Michela

a Université Pierre et Marie Curie, Paris, France
b Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow, Russia
English version PDF (590 kB) Citations (4)
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DOI: https://doi.org/10.1070/RM2012v067n06ABEH004818
Abstract: This paper proposes direct and inverse results for the Dirichlet and Dirichlet-to-Neumann problems for complex curves with nodal type singularities. As an application, it gives a method for reconstructing the conformal structure of a compact surface of $\mathbb R^3$ with constant scalar conductivity from electric current density measurements in a neighbourhood of one of its points.
Bibliography: 23 titles.
Keywords: conformal structure, Riemann surface, nodal curve, Green function, inverse Dirichlet-to-Neumann problem.
Received: 31.10.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 6(408), Pages 101–124
DOI: https://doi.org/10.4213/rm9501
Bibliographic databases:
Document Type: Article
UDC: 517.54
MSC: 32D15, 32C25, 32V15, 35R30, 58J32
Language: English
Original paper language: Russian
Citation: G. Henkin, V. Michel, “Inverse Dirichlet-to-Neumann problem for nodal curves”, Uspekhi Mat. Nauk, 67:6(408) (2012), 101–124; Russian Math. Surveys, 67:6 (2012), 1069–1089
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v67/i6/p101
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:243
    English version PDF:26
    References:79
    First page:38
     
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