Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory

Kim, Yong-Jung; Lee, Min

doi:10.1090/qam/1368

Authors: Yong-Jung Kim and Min Gi Lee
Journal: Quart. Appl. Math. 73 (2015), 419-433
MSC (2010): Primary 78A30; Secondary 65N21
DOI: https://doi.org/10.1090/qam/1368
Published electronically: June 23, 2015
MathSciNet review: 3400751
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Abstract | References | Similar Articles | Additional Information

Abstract: We 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.

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