• Media type: Text; E-Article
  • Title: A shape calculus analysis for tracking type formulations in electrical impedance tomography
  • Contributor: Eppler, Karsten [Author]
  • Published: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2009
  • Language: English
  • DOI: https://doi.org/10.1515/jiip.2009.043
  • ISSN: 0928-0219
  • Keywords: article ; electrical impedance tomography -- shape calculus -- boundary integral equations -- ill-posed problems -- two norm discrepancy
  • Origination:
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  • Description: In the paper [17], 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.