Low frequency asymptotics for the reduced wave equation in two‐dimensional exterior spaces
Peter Christian Werner · Mathematical Methods in the Applied Sciences · 1986
Abstract We consider the Dirichlet problem for the reduced wave equation ΔUx + x2Ux = 0 in a two‐dimensional exterior domain with boundary C, where C consists of a finite number of smooth closed curves C1,…,Cm. The question of interest is the behavior of Ux as ϰ → 0. We show that U converges to the solution of the corresponding exterior Dirichlet problem of potential theory if the boundary data converge to a limit uniformly on C. This generalizes a well‐known result of R. C. MacCamy for the case m = 1.