Reconstructing Conductivity from Minimal Internal Data
Seminar Room 1, Newton Institute
AbstractWe consider the problem of recovering the electric conductivity of a body from knowledge of the magnitude of one curent in the interior. We show that the corresponding equipotential surfaces are area minimizing in a conformal metric determined by the given data, prove identifiability and give numerical reconstructions. We also extend the uniqueness results to the case when the object may contain perfectly conducting and/or insulating regions. (Joint work with Amir Moradifam, Alexandru Tamasan and Alexandre Timonov.)
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