On the neumann problem for the Helmholtz equation in a plane angle

We prove that the solution of the Neumann problem for the Helmholtz equation in a plane angle Omega with boundary conditions from the space H-1/2(Gamma), where Gamma is the boundary of Omega, which is provided by the well-known Sommerfeld integral, belongs to the Sobolev space H-1(Omega) and depends continuously on the boundary values. To this end, we use another representation of the solution given by the inverse two-dimensional Fourier transform of an analytic function depending on the Cauchy data of the solution. Copyright (C) 2000 John Wiley & Sons, Ltd.