and we find (classical) solutions of (6), in and in . The physical interface conditions are well known, it is observed that the normal component of and the tangential component of are continuous. We will demonstrate that these conditions are quite naturally included in a variational formulation using a continuous vector potential . On one hand,
implies the ''strong'' first interface condition
On the other hand, it follows from
and the line integrals over the interface will cancel out, i.e., the second interface condition is contained in a ''weak'' sense in the variational formulation. Thus, the variational formulation presented in the following is the correct representation of the physical behaviour. We remark that the variational formulation can be derived from the energy functional of the magnetic field,
too, and that the second interface condition is not included so naturally if a formulation is used.