  We determine the ground state properties of inhomogeneous mixtures of bosons
and fermions in cubic lattices by studying the Bose-Fermi Hubbard model
including parabolic confining potentials. We present the exact solution in the
limit of vanishing hopping (ultradeep lattices) and study the resulting domain
structure of composite particles. For finite hopping we determine the domain
boundaries between Mott-insulator plateaux and hopping-dominated regions for
lattices of arbitrary dimensionality within perturbation theory. The results
are compared with a new numerical method that is based on a Gutzwiller
variational approach for the bosons and an exact treatment for the fermions.
The findings can be applied as a guideline for future experiments with trapped
atomic Bose-Fermi mixtures in optical lattices.
