  We study the current and charge distribution of a two dimensional electron
gas under strong perpendicular magnetic fields within the linear response
regime. We show within a self-consistent screening theory that incompressible
strips with integer values of local Landau-level filling factor exist for
finite intervals of the magnetic field strength $B$. Within an essentially
local conductivity model, we find that the current density in these $B$
intervals is confined to the incompressible strips of vanishing local
longitudinal resistivity. This leads to vanishing longitudinal and exactly
quantized Hall resistance, and to a nice agreement of the calculated Hall
potential profiles with the measured ones.
