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
Dept. of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia
Received 23 September 1996; Revised 17 April 1997
Copyright © 1998 P. A. Krutitskii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.