On the form of constitutive equations in electrodynamics

A comparative analysis of various forms of the Maxwell equations for condensed matter is presented. It is shown that the so-called Casimir form contains enough information to solve any electromagnetic problem. The Landau–Lifshitz form intended for describing media with spatial dispersion requires an additional constitutive equation for the surface current, which does not set an additional boundary condition but acts as a replacement of usual Maxwell's continuity conditions for tangential field components.