On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc

Abstract

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.