  We investigate the speed of approach to Maxwellian equilibrium for a
collisionless gas enclosed in a vessel whose wall are kept at a uniform,
constant temperature, assuming diffuse reflection of gas molecules on the
vessel wall. We establish lower bounds for potential decay rates assuming
uniform $L^p$ bounds on the initial distribution function. We also obtain a
decay estimate in the spherically symmetric case. We discuss with particular
care the influence of low-speed particles on thermalization by the wall.
