The Neumann-to-Dirichlet map in two dimensions

For the two-dimensional Schrödinger equation in a bounded domain, we prove uniqueness of the determination of potentials in Wp1(Ω), p>2 in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set Γ˜ of the boundary and observe the corresponding Dirichlet da...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 281; pp. 578 - 593
Main Authors Imanuvilov, O.Yu, Uhlmann, Gunther, Yamamoto, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2015
Subjects
Complex geometrical optics solutions
Neumann-to-Dirichlet map
Complex geometrical optics solutions
Neumann-to-Dirichlet map
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Summary:For the two-dimensional Schrödinger equation in a bounded domain, we prove uniqueness of the determination of potentials in Wp1(Ω), p>2 in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set Γ˜ of the boundary and observe the corresponding Dirichlet data on Γ˜. An immediate consequence is that one can uniquely determine a conductivity in Wp3(Ω) with p>2 by measuring the voltage on an open subset of the boundary corresponding to a current supported in the same set.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.03.026