  We study bosonic atoms on the p-band of a two dimensional optical square
lattice in the presence of a confining trapping potential. Using a mean-field
approach, we show how the anisotropic tunneling for p-band particles affects
the cloud of condensed atoms by characterizing the ground state density and the
coherence properties of the atomic states both between sites and atomic
flavors. In contrast to the usual results based on the local density
approximation, the atomic density can become anisotropic. This anisotropic
effect is especially pronounced in the limit of weak atom-atom interactions and
of weak lattice amplitudes, i.e. when the properties of the ground state are
mainly driven by the kinetic energies. We also investigate how the trap
influences known properties of the non-trapped case. In particular, we focus on
the behavior of the anti-ferromagnetic vortex-antivortex order, which for the
confined system, is shown to disappear at the edges of the condensed cloud.
