Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory
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AbstractWe show the well-posedness of the conductivity image reconstruction problem with a single set of interior electrical current data and boundary conductivity data. Isotropic conductivity is considered in two space dimensions. Uniqueness for similar conductivity reconstruction problems has been known for several cases. However, the existence and the stability are obtained in this paper for the first time. The main tool of the proof is the method of characteristics of a related curl equation.
CitationWell-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory 2015, 73 (3):419 Quarterly of Applied Mathematics
PublisherAmerican Mathematical Society (AMS)
JournalQuarterly of Applied Mathematics