When boundary conditions of higher order than the first are applied to an edged structure such as a wedge or half plane, difficulties occur associated with the uniqueness and reciprocity of the solution. These are illustrated in the case of a plane wave incident on a half plane subject to arbitrary second order boundary conditions different on the two faces. Using an extension of the standard Maliuzhinets method, it is shown how reciprocity can be explicitly enforced, and a solution is then obtained involving an arbitrary constant. The constant is related to the surface value of the field at the edge, and this additional information is necessary for a unique solution.
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