The Helmholtz equation in a non-smooth inclusion

In this paper, we study the Helmholtz equation in a non-smooth inclusion, i.e., in a doubly connected bounded domain B in R2 with boundary ∂B that consists of two disjoint closed curves Γ and Γ0. The existence and uniqueness of a solution to the Helmholtz equation for mixed boundary conditions on Γ are obtained by using Riesz-Fredholm theory.