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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 D i , u=u e in D e , u=u i in D i , χ (D) the characteristic function of D, a=1+(μ-1)χ(D), c=1+(ρ-1)χ(D). Further, let u be a solution of div(au)+k 2 cu=0, satisfying u i =u e , u e /N=μu i /N on D, u e (x)=exp(ix·ξ+u e 0 (x), |ξ|=k, r (n-1)/2 (u e 0 /r-iku e 0 )0 for r. The author applies ideas of Nachman, Sylvester, Uhlmann and own results for this special problem under consideration.
Reviewer: G.Anger (Berlin)

35R30Inverse problems for PDE
35P25Scattering theory (PDE)
35J10Schrödinger operator
78A40Waves and radiation (optics)