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A Global Uniqueness Theorem for an Inverse Boundary Value Problem

John Sylvester and Gunther Uhlmann
Annals of Mathematics
Second Series, Vol. 125, No. 1 (Jan., 1987), pp. 153-169
Published by: Annals of Mathematics
DOI: 10.2307/1971291
Stable URL: http://www.jstor.org/stable/1971291
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Global Uniqueness Theorem for an Inverse Boundary Value Problem
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Abstract

In this paper, we show that the single smooth coefficient of the elliptic operator Lγ = ∇ · γ∇ can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region $\Omega \subseteq R^n, n \geq 3.$ From a physical point of view, we show that an isotropic conductivity can be determined by steady state measurements at the boundary.

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