Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 297  305 (1999) 

On the Low Wave Number Behavior of TwoDimensional Scattering Problems for an Open ArcR. KressR. Kress: Inst. für Num. und Ang. Math. der Univ., Lotzestr. 1618, D  37083 GöttingenAbstract: The low wave number asymptotics for the solution of the Dirichlet problem for the twodimensional Helmholtz equation in the exterior of an open arc is analyzed via a singlelayer 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. Keywords: Helmholtz equation, exterior boundary value problems, integral equation methods, low wave number limits, cosine substitution Full text of the article:
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