Steady-state wave propagation problem in inhomogeneous anisotropic media including crystals (Q1120720)

The steady-state wave propagation problem \((\Lambda -\lambda)v=g,\) \(x\in \Omega\), in an exterior domain is studied. To handle inhomogeneous media including crystals the assumption \(\Lambda =E(x)^{-1}\{\Lambda^ 0+B(x)\}\) where \(\Lambda^ 0\) is the differential operator of the homogeneous media problem (E pos. def., B continuous) and the restriction \(v\in N(x)\), \(x\in \partial \Omega\) are included. Here, N(x) describes a subspace of \({\mathbb{C}}^ m\) depending smoothly on \(x\in \partial \Omega\). Further, radiation conditions are assumed. The main result is the genealization of the Rellich uniqueness theorem for homogeneous media to the equation stated above. Further, the eigenfunction expansion and the limiting absorption principle are derived. Several of the proofs are carried out in analogy to \textit{J. R. Schulenberger} and \textit{C. H. Wilcox} [Arch. Ration. Mech. Anal. 46, 280- 320 (1972; Zbl 0252.47047)].