The Resistive and Conductive Problems for the Exterior Helmholtz Equation

Abstract

The existence, uniqueness, and continuous dependence of solutions of the Helmholtz equation, which are subject to either resistive or conductive conditions at the boundary of a closed smooth scatterer, are considered. A boundary integral equation of the second kind for each problem whose unique solution is the trace on the boundary of the unique solution of that problem is devised. Continuous dependence results are proven using the integral equations.