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

### R. Kress

Georg-August-Universität Göttingen, Germany

## 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.

## 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

DOI 10.4171/ZAA/883