  The distribution of counterions and the electrostatic interaction between two
similarly charged dielectric slabs is studied in the strong coupling limit.
Dielectric inhomogeneities and discreteness of charge on the slabs have been
taken into account. It is found that the amount of dielectric constant
difference between the slabs and the environment, and the discreteness of
charge on the slabs have opposing effects on the equilibrium distribution of
the counterions. At small inter-slab separations, increasing the amount of
dielectric constant difference increases the tendency of the counterions toward
the middle of the intersurface space between the slabs and the discreteness of
charge pushes them to the surfaces of the slabs. In the limit of point charges,
independent of the strength of dielectric inhomogeneity, counterions distribute
near the surfaces of the slabs. The interaction between the slabs is attractive
at low temperatures and its strength increases with the dielectric constant
difference. At room temperature, the slabs may completely attract each other,
reach to an equilibrium separation or have two equilibrium separations with a
barrier in between, depending on the system parameters.
