Inverse scattering problem for transparent obstacles

Source abstract

Let K ⊂ ℝ 3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K . Set We wish to study the filtered scattering amplitude, related to the transmission problem Here w ± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω; . The function α(x) ∈ C ∞ ( K¯ ), called the index of refraction, has the property α( x ) > 0 for x ∈ K¯ .