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

Yong-Jung Kim, Min-Gi Lee

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)419-433
Number of pages15
JournalQuarterly of Applied Mathematics
Volume73
Issue number3
DOIs
StatePublished - Jun 23 2015

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