Far-field patterns for time-harmonic acoustic plane waves in an inhomogeneous medium

Abstract

This paper is concerned with the class of far-field patterns corresponding to the scattering of time-harmonic acoustic plane waves by an inhomogeneous medium which have ρ i ( x)>0 continuously differentiable density. This class is shown to be complete in L 2(∂ Ω) (where ∂ Ω is the unit sphere) under the same restriction. The existence of a unique weak solution to the interior transmission problem is also established.