Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

Authors: Yong-Jung Kim and Min Gi Lee
Journal: Quart. Appl. Math. 73 (2015), 419-433
MSC (2010): Primary 78A30; Secondary 65N21
Published electronically: June 23, 2015
MathSciNet review: 3400751
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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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Yong-Jung Kim
Affiliation: Department of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of Korea, and National Institute of Mathematical Sciences, Daejeon 305-811, Republic of Korea
Email: yongkim@kaist.edu

Min Gi Lee
Affiliation: Computer, Electrical and Mathematical Sciences and Engineering, 4700 King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia
Email: mgleemail@gmail.com

DOI: https://doi.org/10.1090/qam/1368
Received by editor(s): May 14, 2013
Published electronically: June 23, 2015
Additional Notes: This research was supported by the project of National Junior Research Fellowship of the National Research Foundation of Korea under grant number 2011-0013447.
Article copyright: © Copyright 2015 Brown University

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