A Revisit of the Velocity Averaging Lemma: On the Regularity of Stationary Boltzmann Equation in a Bounded Convex Domain

In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded convex domain. Considering the incoming data, with four iterations, we establish regularity in fractional Sobolev space in space variable up to order 1 -.