Abstract
The boundary value problem for the quasistationary magnetic approximation of the time-harmonic Maxwell equations in inhomogeneous media is studied. The considered problem is reduced to the variational problem of determining vector magnetic and scalar electric potentials. The special gauges are discussed, that generalize the Coulomb and Lorenz gauges and allow to formulate the problems of the independent definitions of the vector magnetic potential. The correctness of the problems are established under general conditions on the coefficients. The relation between solutions of the problems with different gauges is studied. The equivalence of the problems for potentials to the original boundary value problem is proved.
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