Comment on A.-P. Calderón's paper: ``On an inverse boundary value problem'' [in *Seminar on Numerical Analysis and its Applications to Continuum Physics* (Rio de Janeiro, 1980), 65-73, Soc. Brasil. Mat., Rio de Janeiro, 1980; MR0590275 (81k:35160)]

Authors:
David Isaacson and Eli L. Isaacson

Journal:
Math. Comp. **52** (1989), 553-559

MSC:
Primary 35R30; Secondary 35K60

MathSciNet review:
962208

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Abstract: Calderón determined a method to approximate the conductivity of a conducting body in (for ) based on measurements of boundary data. The approximation is good in the norm provided that the conductivity is a small perturbation from a constant. We calculate the approximation exactly for the case of homogeneous concentric conducting disks in with different conductivities. Here, the difference in the conductivities is the perturbation. We show that the approximation yields precise information about the spatial variation of , even when the perturbation is large. This ability to distinguish spatial regions with different conductivities is important for clinical monitoring applications.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1989-0962208-X

Article copyright:
© Copyright 1989
American Mathematical Society