Abstract

We consider the regularity of solutions to the stationary linearized Boltzmann equations in bounded C ¹ convex domains in R ³ for gases with cutoff hard potential and cutoff Maxwellian gases. Suppose that a solution has a bounded weighted L ² norm in space and velocity with the weight of collision frequency, which is a typical functional space for existence results for boundary value problems. We prove that this solution is Holder continuous with  order   away from the boundary provided the incoming data have the same regularity and uniformly bounded by a fixed function in velocity with finite weighted L ² norm with the weight of collision frequency. A smoothing effect due to the combination of collision and transport is used in the proof.