  Recent spatially resolved measurements of the electrostatic-potential
variation across a Hall bar in strong magnetic fields, which revealed a clear
correlation between current-carrying strips and incompressible strips expected
near the edges of the Hall bar, cannot be understood on the basis of existing
equilibrium theories. To explain these experiments, we generalize the
Thomas-Fermi--Poisson approach for the self-consistent calculation of
electrostatic potential and electron density in {\em total} thermal equilibrium
to a {\em local equilibrium} theory that allows to treat finite gradients of
the electrochemical potential as driving forces of currents in the presence of
dissipation. A conventional conductivity model with small values of the
longitudinal conductivity for integer values of the (local) Landau-level
filling factor shows that, in apparent agreement with experiment, the current
density is localized near incompressible strips, whose location and width in
turn depend on the applied current.
