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On uniqueness in the inverse transmission scattering problem. (English) Zbl 0728.35148
In this paper uniqueness results are proved for the inverse scattering problems where the unknown scatterer D is a bounded open set and some coefficients of an elliptic equation are unknown as well. Let \(D^ i\) be the bounded open set in \(R^ n\), \(D^ e=R^ n\setminus D^ i\), \(u=u^ e\) in \(D^ e\), \(u=u^ i\) in \(D^ i\), \(\chi\) (D) the characteristic function of D, \(a=1+(\mu -1)\chi (D)\), \(c=1+(\rho -1)\chi (D)\). Further, let u be a solution of \(div(a\nabla u)+k^ 2cu=0\), satisfying \(u^ i=u^ e\), \(\partial u^ e/\partial N=\mu \partial u^ i/\partial N\) on \(\partial D\), \(u^ e(x)=\exp (ix\cdot \xi +u^{e_ 0}(x)\), \(| \xi | =k\), \(r^{(n-1)/2}(\partial u^{e_ 0}/\partial r-iku^{e_ 0})\to 0\) for \(r\to \infty\). The author applies ideas of Nachman, Sylvester, Uhlmann and own results for this special problem under consideration.
Reviewer: G.Anger (Berlin)

35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
78A40 Waves and radiation in optics and electromagnetic theory
Full Text: DOI
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