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 [ L 2 + (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.