  We consider the Boltzmann equation with external fields in strictly convex
domains with diffuse reflection boundary condition. As long as the normal
derivative of external fields satisfy some sign condition on the boundary (1.8)
we construct classical $C^1$ solutions away from the grazing set. As a
consequence we construct solutions of Vlasov-Poisson-Boltzmann system having
bounded derivatives away from the grazing set (weighted $W^{1,\infty}$
estimate). In particular this improves the recent regularity estimate of such
system in weighted $W^{1,p}$ space for $p<6$ in [1].
