Archive for Rational Mechanics and Analysis

, Volume 105, Issue 4, pp 299–326

Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence

  • Avner Friedman
  • Michael Vogelius
Article

DOI: 10.1007/BF00281494

Cite this article as:
Friedman, A. & Vogelius, M. Arch. Rational Mech. Anal. (1989) 105: 299. doi:10.1007/BF00281494

Abstract

We consider an electrostatic problem for a conductor consisting of finitely many small inhomogeneities of extreme conductivity, embedded in a spatially varying reference medium. Firstly we establish an asymptotic formula for the voltage potential in terms of the reference voltage potential, the location of the inhomogeneities and their geometry. Secondly we use this representation formula to prove a Lipschitz-continuous dependence estimate for the corresponding inverse problem. This estimate bounds the difference in the location and in certain geometric properties of two sets of inhomogeneities by the difference in the boundary voltage potentials corresponding to a fixed current distribution.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Avner Friedman
    • 1
    • 2
  • Michael Vogelius
    • 1
    • 2
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolis
  2. 2.Department of MathematicsUniversity of MarylandCollege Park