On an integral equation approach for the exterior Robin problem for the Helmholtz equation

Abstract A boundary integral equation for the exterior Robin problem for Helmholtz's equation is analyzed in this paper. This integral operator is not compact. A proof based on a suitable regularization of this integral operator and the Fredholm alternative for the regularized compact operator was given by other authors. In this paper, we will give a direct existence and uniqueness proof for the boundary non-compact integral equation in the space settings C 1, λ ( S ) and C 0, λ ( S ), where S is a closed bounded smooth surface.