no. 1
Conformal mapping and inverse conductivity problem with one measurement
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 163-177.

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series of numerical examples illustrating the performance of the method.

DOI : 10.1051/cocv:2007006
Classification : 49N45, 49Q10, 30C30
Mots clés : inverse conductivity problem, conformal mapping 
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Dambrine, Marc; Kateb, Djalil. Conformal mapping and inverse conductivity problem with one measurement. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 1, pp. 163-177. doi : 10.1051/cocv:2007006. http://www.numdam.org/articles/10.1051/cocv:2007006/

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