The impedance tomography problem

Author:
A. Boumenir

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3553-3557

MSC (1991):
Primary 47-XX, 39B42, 35R30

DOI:
https://doi.org/10.1090/S0002-9939-03-06942-9

Published electronically:
February 24, 2003

MathSciNet review:
1991768

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Abstract | References | Similar Articles | Additional Information

Abstract: Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explicit formula for the conductivity coefficient in terms of the Dirichlet to Neumann map and the eigenvalues of the Laplacian operator.

**1.**D. E. Edmunds and W. D. Evans, Spectral theory and differential operators, Oxford Mathematical Monographs, Oxford Science Publications, (1987). MR**89b:47001****2.**V. Isakov, Inverse problems for partial differential equations, Applied Math.Sciences, 127, Springer, (1998). MR**99b:35211****3.**A. Katchalov, Y. Kurylev and M. Lassas, Inverse boundary spectral problems, CRC, 123, Boca Raton, (2001).**4.**I. Knowles, Uniqueness for an elliptic inverse problem. SIAM J. Appl. Math. 59, 4, 1356-1370, (1999). MR**2000a:35252****5.**V.Mikhailov, Equations aux derivees partielles, translations MIR editions, Moscow, (1980). MR**82a:35003b****6.**A. Nachman, Global Uniqueness for a two dimensional inverse boundary value problem, Ann. Math. 142, 71-96, (1995). MR**96k:35189****7.**S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem, Inverse Problems 16, 681-699, (2000). MR**2001g:35269****8.**J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math. 125, 153-169, (1987). MR**88b:35205**

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Additional Information

**A. Boumenir**

Affiliation:
Department of Mathematics, State University of West Georgia, Carrollton, Georgia 30118

Email:
boumenir@westga.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-06942-9

Keywords:
Boundary inversion problem,
tomography

Received by editor(s):
May 27, 2002

Received by editor(s) in revised form:
June 24, 2002

Published electronically:
February 24, 2003

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society