A regularization method for the stationary Maxwell equations in an inhomogeneous conducting medium

This paper considers a problem of defining the vector potential of a magnetic field with a non-standard calibration in an inhomogeneous conducting medium. The problem in question is the one with constraints on the right-hand side and on the solution itself. The generalized and regularized statement of this problem without constraints is proposed and substantiated. This statement of the problem is equivalent to the original generalized problem with constraints.