Some remarks on the impedance tomography problem for 3d-manifolds

M.I. Belishev

Some remarks on the impedance tomography problem for 3d-manifolds

Authors

M.I. Belishev Saint-Petersburg, Department of the Steklov Mathematical Institute (POMI), 27 Fontanka, St. Petersburg 191011, Russia.ika, St. Petersburg 19101 1, Russia.

Keywords:

impedance tomography, 3d-manifolds, Betti numbers, harmonic fields, friedrichs decomposition, Elliptic Dirichlet-to-Neumann map

Abstract

We derive the formulas expressing the topological characteristics (Betti numbers) of 3d-manifold with boundary through its Dirichlet-to-Neumann maps associated with scalar and vector harmonic fields.