Abstract
Generalized boundary conditions are characterized by the presence of field derivatives higher than the first, and are designed to improve the simulation of the material properties of a surface. A rather general class of conditions is described and the constraints necessary to ensure a unique solution of the boundary-value problem are then derived. In the case of a planar surface, each boundary condition implies a pair of related transition conditions describing membranes. These are complementary in the sense of Babinet’s principle, and the connection between the total fields in the two problems is shown.
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