Formulation of the Boundary Problem for Electrodynamic Potentials in a Piecewise-Homogeneous Medium.

It is shown that gradient invariance in the determination of the scalar and vectorial electrodynamic potentials permits simplification of the boundary conditions for them at the interface between two linear homogeneous magnetoelectric materials. It permits thus to reduce calculation of the electromagnetic field to a successive solution of two boundary problems - first to the scalar, and then to the vectorial problem. The existence and uniqueness of the solution of these problems is proved and particular cases are discussed.