Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A Calderón problem with frequency-differential data in dispersive media


Authors: Sungwhan Kim and Alexandru Tamasan
Journal: Proc. Amer. Math. Soc. 144 (2016), 1265-1276
MSC (2010): Primary 35R30, 35J65, 65N21
DOI: https://doi.org/10.1090/proc12788
Published electronically: July 8, 2015
MathSciNet review: 3447677
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of identifying a complex valued coefficient $ \gamma (x,\omega )$ in the conductivity equation $ \nabla \cdot \gamma (\cdot ,\omega )\nabla u(\cdot ,\omega )=0$ from knowledge of the frequency differentials of the Dirichlet-to-Neumann map. For a frequency analytic $ \gamma (\cdot ,\omega )=\sum _{k=0}^\infty (\sigma _k+i\epsilon _k)\omega ^k$, in three dimensions and higher, we show that $ \left .\frac {d^j}{d\omega ^j}\Lambda _{\gamma (\cdot ,\omega )}\right \vert _{\omega =0}$ for $ j=0,1,\dots ,N$ recovers $ \sigma _0,\dots , \sigma _N$ and $ \epsilon _1,\dots ,\epsilon _N$. This problem arises in frequency differential electrical impedance tomography of dispersive media.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35R30, 35J65, 65N21

Retrieve articles in all journals with MSC (2010): 35R30, 35J65, 65N21


Additional Information

Sungwhan Kim
Affiliation: Division of Liberal Arts, Hanbat National University, Korea
Email: sungwhan@hanbat.ac.kr

Alexandru Tamasan
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: tamasan@math.ucf.edu

DOI: https://doi.org/10.1090/proc12788
Keywords: Calder\'on problem, frequency differential electrical impedance tomography, complex geometrical optics
Received by editor(s): October 6, 2014
Received by editor(s) in revised form: March 22, 2015
Published electronically: July 8, 2015
Additional Notes: The second author was supported in part by the NSF Grant DMS 1312883.
Communicated by: Catherine Sulem
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society