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.