International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 2, Pages 209-216
doi:10.1155/S0161171298000301
The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves
P.A. Krutitskii
Dept. of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia
Abstract
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.