The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves - P. A. Krutitskii (International Journal of Mathematics and Mathematical Sciences)
The Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. Our approach holds for both internal and external domains.