  We investigate some aspects of the Bose-Einstein condensation (BEC) of
quantum gases in the presence of inhomogeneous conditions. We consider
three-dimensional (3D) quantum gases trapped by an external potential when the
temperature is sufficiently low to show a BEC phase region around the center of
the trap. If the trap is sufficiently large, different phases may coexist in
different space regions, when moving from the center of the trap. We show that
the quantum gas develops a peculiar critical behavior at the boundary of the
BEC region, whose scaling behavior is controlled by the universality class of
the homogenous BEC transition. We provide numerical evidence of this
phenomenon, for lattice atomic gases modeled by the 3D Bose-Hubbard
Hamiltonian.
