Effective Maxwell equations for finite planar samples in QHE regime

Effective Maxwell equations for the mean quantum electromagnetic field in planar samples in QHE regime are investigated. Boundary conditions to be satisfied by the mean field intensities at the filamentary boundaries (edges) are determined. For ideal strictly 2D samples embedded in real 3D space, these constraints imply that the total filamentary charge at the boundaries (the free plus polarization terms) and current densities identically vanish at all times. In the static limit the exact quantization of the Hall resistance of samples of arbitrary form, directly follows from the boundary condition. The equations for the electromagnetic response in a neighborhood of the edge of a half-plane in QHE regime are solved. The system exhibits a weak diamagnetic response and inhomogeneous charge and current distributions develop in the sample.