  We present a theoretical description of the thermal fluctuations in a
solid-supported stack of lipid bilayers, for the case of vanishing surface
tension $\gamma = 0$ and in the framework of continuous smectic elasticity. The
model is successfully used to model the reflectivity profile of a thin (16
bilayers) DMPC sample under applied osmotic pressure and the diffuse scattering
from a thick (800 bilayers) stack. We compare our model to previously existing
theories.
