  We discuss effects of particle interaction on Bose condensation in
inhomogeneous traps with and without optical lattice. Interaction pushes normal
particles away from the condensate droplet, which is located in the center of
the trap, towards the periphery of the trap where the trapping potential is
large. In the end, the remaining normal particles are squeezed to a quasi-2D
shell around the condensate droplet thus changing the effective dimensionality
of the system. In the absence of the optical lattice the index in the
temperature dependence of the condensate density at the later stages of the
process is close to 2 with a weak dependence on the number of trapped
particles. In the presence of the lattice inside the trap this index acquires a
strong dependence on the number of particles inside the trap and gradually
falls from a 3D to a 2D value with an increase in the number of particles. This
change in index is explained by the lattice-driven spread of the condensate
droplet and the localization of the narrow band particles by the trap
potential.
