Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 0.466
Source Normalized Impact per Paper (SNIP): 1.251

Mathematical Citation Quotient 2013: 0.51



A shape calculus analysis for tracking type formulations in electrical impedance tomography

K. Eppler1

1Institute of Numerical Mathematics, TU Dresden, Zellescher Weg 12–14, 01062 Dresden, Germany. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 8, Pages 733–751, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.043, November 2009

Publication History

Published Online:


In the paper [Eppler and Harbrecht, Control & Cybernetics 34: 203–225, 2005], the authors investigated the identification of an obstacle or void of perfectly conducting material in a two-dimensional domain by measurements of voltage and currents at the boundary. In particular, the reformulation of the given nonlinear identification problem was considered as a shape optimization problem using the Kohn and Vogelius criterion. The compactness of the complete shape Hessian at the optimal inclusion was proven, verifying strictly the ill-posedness of the identification problem. The aim of the paper is to present a similar analysis for the related least square tracking formulations. It turns out that the two-norm-discrepancy is of the same principal nature as for the Kohn and Vogelius objective. As a byproduct, the necessary first order optimality condition are shown to be satisfied if and only if the data are perfectly matching. Finally, we comment on possible consequences of the two-norm-discrepancy for the regularization issue.

Key words.: Electrical impedance tomography; shape calculus; boundary integral equations; ill-posed problems; two norm discrepancy

Comments (0)

Please log in or register to comment.