  We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard
model with a quadratic, confining potential. In the absence of this potential,
our mean-field theory yields the phase diagram of the homogeneous extended
Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes
of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the
plane of the chemical potential (\mu) and on-site repulsion (U); we present
phase diagrams for representative values of V, the repulsive energy for bosons
on nearest-neighbor sites. We demonstrate that, when the confining potential is
present, superfluid and density-wave order parameters are nonuniform; in
particular, we obtain, for a few representative values of parameters, spherical
shells of SF, MI, DW, and SS phases. We explore the implications of our study
for experiments on cold-atom dipolar condensates in optical lattices in a
confining potential
