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

Handle URI:
http://hdl.handle.net/10754/583036
Title:
Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory
Authors:
Kim, Yong-Jung; Lee, Min-Gi ( 0000-0002-1953-2547 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory 2015, 73 (3):419 Quarterly of Applied Mathematics
Publisher:
American Mathematical Society (AMS)
Journal:
Quarterly of Applied Mathematics
Issue Date:
23-Jun-2015
DOI:
10.1090/qam/1368
Type:
Article
ISSN:
0033-569X; 1552-4485
Additional Links:
http://www.ams.org/qam/2015-73-03/S0033-569X-2015-01368-9/; http://amath.kaist.ac.kr/papers/Kim/18.pdf
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKim, Yong-Jungen
dc.contributor.authorLee, Min-Gien
dc.date.accessioned2015-12-01T07:50:45Zen
dc.date.available2015-12-01T07:50:45Zen
dc.date.issued2015-06-23en
dc.identifier.citationWell-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory 2015, 73 (3):419 Quarterly of Applied Mathematicsen
dc.identifier.issn0033-569Xen
dc.identifier.issn1552-4485en
dc.identifier.doi10.1090/qam/1368en
dc.identifier.urihttp://hdl.handle.net/10754/583036en
dc.description.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.en
dc.language.isoenen
dc.publisherAmerican Mathematical Society (AMS)en
dc.relation.urlhttp://www.ams.org/qam/2015-73-03/S0033-569X-2015-01368-9/en
dc.relation.urlhttp://amath.kaist.ac.kr/papers/Kim/18.pdfen
dc.rightsArchived with thanks to Quarterly of Applied Mathematicsen
dc.titleWell-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theoryen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalQuarterly of Applied Mathematicsen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Mathematical Sciences, KAIST, Daejeon 305-701, Republic of Korea, and National Institute of Mathematical Sciences, Daejeon 305-811, Republic of Koreaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorLee, Min-Gien
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