  Based on a recent $L^{6}-L^{\infty}$ approach, validity of diffusive limit is
established for both steady and unsteady Boltzmann equation in the presence of
the classical Maxwell boundary condition for a full arrange of the
accommodation coefficient $0 \leq \alpha \leq 1$. A general stretching method
is developed to control bouncing trajectories for the specular reflection with
$\alpha=0$ in the hydrodynamic limit, and refined estimates uniform with
respect to $0 \leq \alpha\leq 1$ for the macroscopic distribution $\mathbf{P}f$
are derived.
