The low wave number asymptotics for the solution of the Dirichlet problem for the two-dimensional Helmholtz equation in the exterior of an open arc is analyzed via a single-layer integral equation approach. It is shown that the solutions to the Dirichlet problem for the Helmholtz equation converge to a solution of the Dirichlet problem for the Laplace equation as the wave number tends to zero provided the boundary values converge.
Cite this article
R. Kress, On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc. Z. Anal. Anwend. 18 (1999), no. 2, pp. 297–305