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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.
@article{COCV_2007__13_1_163_0,
author = {Dambrine, Marc and Kateb, Djalil},
title = {Conformal mapping and inverse conductivity problem with one measurement},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {163--177},
publisher = {EDP-Sciences},
volume = {13},
number = {1},
year = {2007},
doi = {10.1051/cocv:2007006},
mrnumber = {2282107},
zbl = {1136.49026},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007006/}
}
TY - JOUR AU - Dambrine, Marc AU - Kateb, Djalil TI - Conformal mapping and inverse conductivity problem with one measurement JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 163 EP - 177 VL - 13 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007006/ DO - 10.1051/cocv:2007006 LA - en ID - COCV_2007__13_1_163_0 ER -
%0 Journal Article %A Dambrine, Marc %A Kateb, Djalil %T Conformal mapping and inverse conductivity problem with one measurement %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 163-177 %V 13 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007006/ %R 10.1051/cocv:2007006 %G en %F COCV_2007__13_1_163_0
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
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