  Using mean-field theory, we study the equilibrium properties of boson-fermion
mixtures confined in a harmonic pancake-shaped trap at zero temperature. When
the modulus of the s-wave scattering lengths are comparable to the mixture
thickness, two-dimensional scattering events introduce a logarithmic dependence
on density in the coupling constants, greatly modifying the density profiles
themselves. We show that for the case of a negative boson-fermion
three-dimensional s-wave scattering length, the dimensional crossover
stabilizes the mixture against collapse and drives it towards spatial demixing.
