Transmission problems for the Helmholtz equation

Abstract

A straightforward treatment of these problems is given which appears to avoid many of the previously encountered difficulties. Admittedly some generality is lost by assuming that the various associated parameters ki are not space dependent within their respective domains of definition, Di. Nevertheless, by means of the approach offered here, such problems can be analyzed in just one function space; more general existence and uniqueness theorems can be obtained; there is no need to regularize the operators involved; and, above all, the solutions can be expressed in terms of certain boundary integral equations which, computationally, offer good prospects.