  We analyze the macroscopic dynamics of a Bose gas axially confined in an
optical lattice with a superimposed harmonic trap, taking into account weak
tunneling effect. Our results show that upon transition to the
quasi-two-dimensional (2D) regime of the trapped gas, the 3D equation of state
and equilibrium density profile acquire corrections from 2D many-body effects.
The corresponding frequency shift in the transverse breathing mode is
accessible within current facilities, suggesting a direct observation of
dimensional effects. Comparisons with other relevant effects are also
presented.
