1999/02/14 by Willi Jager, Yoshimi Saito
Mathematics · #math.SP
published as Forum Mathematicum 9 (1997) 29-60 · 36 pages; no figures
arxiv created 1999/02/14 · arxiv updated 2009/11/30
Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step function with a surface S of discontinuity (the separation surface). So far the stratified media in which the separating surface S consists of paralell planes have been vigorously studied. Also the case where S has a cone shape has been discussed. In this work we shall deal with a new type of discontinuity which we call cylindrical discontinuity. Under this condition we shall use the limiting absorption method to prove that H is absolute continuous. Our method is based on a apriori estimates of radiation condition term.