On Beltrami fields with nonconstant proportionality factor on the plane

We consider the equation rotB+aB=0 (1) in the plane with a being a real-valued function and show that it can be reduced to a Vekua equation of a special form. In the case when a depends on one Cartesian variable a complete system of exact solutions of the Vekua equation and hence of equation (1) is constructed based on L. Bers theory of formal powers.

On the solution of the static Maxwell system in axially symmetric inhomogeneous media

We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.