Sommerfeld Half-plane Problems with Higher Order Boundary Conditions

Sommerfeld-type diffraction problems for a half-plane with arbitrary n-th order generalized impedance boundary conditions arc examined in a Sobolev space setting. The corresponding boundary-transmission problems for the two dimensional Helmholtz equation are shown to be well-posed in a family of Sobolev spaces with finite energy norms, through a reduction to equivalent systems of boundary integral equations of Wiener-Hopf type in L₂⁺ (IR)]². Formulas for the solutions as well as the so-called edge conditions arc obtained for any n, by explicit canonical generalized factorization of the presymbols of the associated Wiener-Hopf operators.