The Helmholtz equation in a non-smooth inclusion Original Research Article

In this paper, we study the Helmholtz equation in a non-smooth inclusion, i.e., in a doubly connected bounded domain BB in R2R2 with boundary ∂B∂B that consists of two disjoint closed curves ΓΓ and Γ0Γ0. The existence and uniqueness of a solution to the Helmholtz equation for mixed boundary conditions on ΓΓ are obtained by using Riesz–Fredholm theory.