The Neumann problem for the dissipative Helmholtz equation in a connected plane region with cuts is studied. The existence of classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. It means that the solution can be computed by standard codes.
Cite this article
P.A. Krutitskii, The Neumann Problem for the 2-D Helmholtz Equation in a Multiply Connected Domain with Cuts. Z. Anal. Anwend. 16 (1997), no. 2, pp. 349–361DOI 10.4171/ZAA/766