Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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 $ \sigma $ of a conducting body in $ {R^n}$ (for $ n \geq 2$) based on measurements of boundary data. The approximation is good in the $ {L_\infty }$ 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 $ {R^2}$ 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 $ \sigma $, 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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Article copyright: © Copyright 1989 American Mathematical Society