A Calderón Problem With Frequency-Differential Data In Dispersive Media

Keywords

Calderón problem; Complex geometrical optics; Frequency differential electrical impedance tomography

Abstract

We consider the problem of identifying a complex valued coefficient γ(x, ω) in the conductivity equation ∇ · γ(·, ω)∇u(·, ω) = 0 from knowledge of the frequency differentials of the Dirichlet-to-Neumann map. For a frequency analytic γ(·, ω) = Σ∞k=0(σk + iεk)ωk, in three dimensions and higher, we show that dj/dωj Λγ(·,ω)│ω=0 for j = 0, 1, …,N recovers σ0, …, σN and 0 1, …, εN. This problem arises in frequency differential electrical impedance tomography of dispersive media.

Publication Date

3-1-2016

Publication Title

Proceedings of the American Mathematical Society

Volume

144

Issue

3

Number of Pages

1265-1276

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/proc12788

Socpus ID

84954517748 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84954517748

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