Abstract

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			We revisit the asymptotic formulas originally derived by Cedio-Fengya, Moskow, and Vogelius [Inverse Problems, 14, 1998, 553-595] and Friedman and Vogelius [Arch. Rational Mech. Anal., 105, 1989, 299-326]. These formulas concern the perturbation in the voltage potential caused by the presence of diametrically small conductivity inhomogeneities. We significantly extend the validity of the previously derived formulas, by showing that they are asymptotically correct, uniformly with respect to the conductivity of the inhomogeneities. We also extend the earlier formulas by allowing the conductivities of the inhomogeneities to be completely arbitrary $L^\infty$, positive definite, symmetric matrix-valued functions. We briefly discuss the relevance of the uniform asymptotic validity, and the admission of arbitrary anisotropically conducting inhomogeneities, as far as applications of these perturbation formulas to ``approximate cloaking'' are concerned. View/Download Publication in pdf format Back to Preprint list Michael Vogelius 2-13-98