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Zbl 0805.35154
Hähner, Peter
A uniqueness theorem for a transmission problem in inverse electromagnetic scattering. (English)
[J] Inverse Probl. 9, No.6, 667-678 (1993). ISSN 0266-5611

The author studies an inverse problem for the inhomogeneous Maxwell equations. It is assumed that there exists a bounded set $D \subset \bbfR\sp 3$ such that outside of $D$ the electric permittivity $\varepsilon$ and the magnetic permeability $\mu$ are constant, and that these quantities and the electric conductivity $\sigma$ change discontinuously across $\partial D$ and are inhomogeneous in $D$. It is moreover assumed that $\sigma$ vanishes outside $D$, but is not identically zero inside $D$.\par The author proves in a first step that if for two given inhomogeneous media the far field patterns coincide for all incoming plane waves, then the jump discontinuities $\partial D\sb 1$ and $\partial D\sb 2$ coincide. Starting from this result, he proves in a second step that under weak conditions also the quantities $\mu, \varepsilon$ and $\sigma$ are uniquely defined by the far field pattern of the solution.\par The proof of this second result is based on ideas from the fundamental paper of {\it J. Sylvester} and {\it G. Uhlmann} [Ann. Math., II. Ser. 125, 153-169 (1987; Zbl 0625.35078)].
[H.-D.Alber (Darmstadt)]

MSC 2000:: *35R30 Inverse problems for PDE
35P25 Scattering theory (PDE)
35Q60 PDE of electromagnetic theory and optics
78A45 Diffraction, scattering (optics)

Keywords: Maxwell equations; inhomogeneous media; far field patterns; jump discontinuities

Citations: Zbl 0625.35078

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