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