Unusual boundary conditions at an interface (EM theory)

The derivation of electromagnetic boundary conditions at an interface by applying Gauss´ divergence theorem to a flat pillbox or Stokes´ curl theorem to a narrow contour is considered for two types of unusual boundary condition. One is an electric field discontinuity and the other is a double layer of current. It is suggested that the usual continuity proofs, based on pillboxes and contours of vanishing dimension, must be handled with care. Specifically, a ´ delta function´ behavior of certain components along the normal is possible.<>