  A theory of heterostructures comprised of LaTiO$_3$ (a Mott insulator) and
SrTiO$_3$ (a band insulator) is presented. The band structure of the Ti $d$%
-electrons is treated with a nearest neighbor tight-binding approximation; the
electric fields arising from the La$^{3+}$/Sr$^{2+}$ charge difference and the
carriers are treated within a Hartree approximation; and the on-site
interactions are treated by unrestricted Hartree-Fock. The phase diagram as a
function of interaction strength and layer number is determined and predictions
are made for optical conductivity experiments. A note worthy finding is that
the edges of the heterostructure are generally metallic.
