The equivalence of the combined interior and exterior scattering problems with the Maxwell equations and boundary equations has been demonstrated [ J. Opt. Soc. Am. B 68, 602– 610 ( 1978)]. The expressions for the fields inside and outside the medium were coupled through certain nonlocal boundary conditions that were shown to be generalizations of the Ewald–Oseen extinction theorem. I consider the Maxwell equations in the sense of generalized functions and obtain, without the use of potentials, expressions for the regional fields. These expressions involve four unknown surface-vector fields. Two nonlocal vector-boundary conditions are obtained directly from the regional field expressions. Two other local vector-boundary conditions emerge if we consider generalized functions acting on a certain space of test functions whose properties are described.
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