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Erschienen in:
2020 | OriginalPaper | Buchkapitel
1. An Inverse Conductivity Problem in Multifrequency Electric Impedance Tomography
verfasst von : Jin Cheng, Mourad Choulli, Shuai Lu
Erschienen in: Inverse Problems and Related Topics
Verlag: Springer Singapore
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Abstract
We deal with the problem
of determining the shape of an inclusion embedded in a homogenous background medium. The multifrequency electrical impedance tomography is used to image the inclusion. For different frequencies, a current is injected at the boundary and the resulting potential is measured. It turns out that the function describing the potential solves an elliptic equation in divergence form with discontinuous leading coefficient. For this inverse problem we aim to establish a logarithmic type stability estimate. The key point in our analysis consists in reducing the original problem to that of determining an unknown part of the inner boundary from a single boundary measurement. The stability estimate is then used to prove uniqueness results. We also provide an expansion of the solution of the BVP under consideration in the eigenfunction basis of the Neumann–Poincaré operator associated to the Neumann–Green function.