  The dynamics of symmetry breaking responsible for lifting the degeneracy of
the Landau levels in the integer quantum Hall effect in graphene is studied in
a low-energy model with the Coulomb interaction. The gap equation for Dirac
quasiparticles is analyzed for both the lowest and higher Landau levels, taking
into account the Landau levels mixing. It is shown that the characteristic
feature of the long-range Coulomb interaction is the decrease of the gap
parameters with increasing the Landau level index $n$ ("running" gaps). The
renormalization (running) of the Fermi velocity as a function of $n$ is also
studied. The solutions of the gap equation reproduce correctly the
experimentally observed integer quantum Hall plateaus in graphene in strong
magnetic fields.
