  We consider stationary and propagating solutions for a Bose-Einstein
condensate in a periodic optical potential with an additional confining optical
or magnetic potential. Using an effective mass approximation we express the
condensate wavefunction in terms of slowly-varying envelopes modulating the
Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we
derive a nonlinear Schr\"{o}dinger equation for propagation of the envelope
function which does not contain the rapid oscillation of the lattice. We then
consider the ground state solutions in detail in the regime of weak, moderate
and strong nonlinear interactions. We describe the form of solution which is
appropriate in each regime, and place careful limits on the validity of each
type of solution.
