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)]
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 by David Isaacson and Eli L. Isaacson PDF
 Math. Comp. 52 (1989), 553559 Request permission
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.References

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Additional Information
 © Copyright 1989 American Mathematical Society
 Journal: Math. Comp. 52 (1989), 553559
 MSC: Primary 35R30; Secondary 35K60
 DOI: https://doi.org/10.1090/S0025571819890962208X
 MathSciNet review: 962208