  We investigate the regularity issue for the diffuse reflection boundary
problem to the stationary linearized Boltzmann equation for hard sphere
potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a
strictly convex bounded domain. We obtain pointwise estimates for first
derivatives of the solution provided the boundary temperature is bounded
differentiable and the solution is bounded. This result can be understood as a
stationary version of the velocity averaging lemma and mixture lemma.
