A Regularization Method for the Quasi-Stationary Maxwell Problem in an Inhomogeneous Conducting Medium

We consider the quasi-stationary Maxwell problem of defining a vector potential of a magnetic field with a non-standard gauging condition in an inhomogeneous conducting medium. The problem in question is the one with constraints on the right-hand side and on the solution itself. A generalized and regularized statement of this problem without constraints is proposed and substantiated. Such a problem statement is equivalent to the original generalized problem with constraints.