The reduced wave equation in layered materials

Abstract

Let H = -(1/m(x))L be the reduced wave operator defined on the N-dimensional Euclidean space, where \f L is the Laplacian. Here m(x) is a positive step function with possible countably infinte surfaces of discontinuity (separating surfaces) under the compatibilty condition (1.12) on each separating surface. These compatibily condition allows us to treat the cases, among others, the separating surfaces are cylinders. The case where the separating surface has only one connected component was discussed in [9]. Also the case where the separating surface is cone-shaped was considered by Eidus [6] and others ([10], [11]). We shall prove the limiting absorption principle for H. Also we shall discuss the case where m(x) is perturbed by a short-range or long-range function.