  We investigate a Bose-Fermi mixture in a three-dimensional optical lattice,
trapped in a harmonic potential. Using Generalized Dynamical Mean-Field theory,
which treats the Bose-Bose and Bose-Fermi interaction in a fully
non-perturbative way, we show that for experimentally relevant parameters a
peak in the condensate fraction close to the point of vanishing Bose-Fermi
interaction is reproduced within a single band framework. We identify two
physical mechanisms contributing to this effect: the spatial redistribution of
particles when the interspecies interaction is changed and the reduced phase
space for strong interactions, which results in a higher temperature at fixed
entropy.
