DOI

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.
Язык оригиналаанглийский
Номер статьи105013
Число страниц14
ЖурналInverse Problems
Том37
Номер выпуска10
DOI
СостояниеОпубликовано - окт 2021

    Предметные области Scopus

  • Теоретические компьютерные науки
  • Обработка сигналов
  • Прикладная математика
  • Прикладные компьютерные науки
  • Математическая физика

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