ON RECONSTRUCTION FROM A PARTIAL KNOWLEDGE OF THE NEUMANN-TO-DIRICHLET OPERATOR

MASARU IKEHATA DEPARTMENT OF MATHEMATICS, FACULTY OF ENGINEERING GUNMA UNIVERSITY, KIRYU 376-8515, JAPAN

1. Problem

Let Ω be a bounded domain in R^{2}. For given two points P and Q on ∂Ω we consider the problem of extracting information about the location of an unknown object D contained in Ω from u(P)−u(Q) of the voltage potentials u induced by infinitely many electric current distributions g on ∂Ω and report a formula for the purpose ([5]).

The method is the enclosure method introduced in [1] and developed in [2], [3], [4], [6].

References

[1] Ikehata, M., Reconstruction of the support function for inclusion from boundary measurements. J. Inverse and Ill-Posed Problems 8(2000), 367–378.

[2] Ikehata, M., Reconstruction of a source domain from the Cauchy data. Inverse Problems 15(1999), 637–645.

[3] Ikehata, M., Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data. Inverse Problems 15(1999), 1231–1241.

[4] Ikehata, M., On reconstruction in the inverse conductivity problem with one measurement. Inverse Problems 16(2000), 785–793.

[5] Ikehata, M., On reconstruction from a partial knowledge of the Neumann-to-Dirichlet operator. Inverse Problems 17(2001), to appear.

[6] Ikehata, M. and Siltanen, S., Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements. Inverse Problems 16(2000), 1043–1052.