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We consider the regularity of stationary solutions to the linearized Boltzmann equations in bounded $C^1$ convex domains in $mathbb{R}^3$ 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 norm for existence results for boundary value problems [R. Esposito et al., Comm. Math. Phys., 323 (2013), pp. 177--239; J. P. Guiraud, J. Mecanique, 9 (1970), pp. 443--490]. We prove that this solution is Holder continuous with order $frac1{2}^-$ away from the boundary provided the incoming data have the same regularity and are uniformly bounded by a fixed function in velocity with finite weighted $L^2$ norm with the weight of collision frequency. The key observation is that the regularity in velocity obtained by collision can be transferred to space by transport and collision. An interplay between velocity and space is introduced in order to realize this observation.

Regularity of Stationary Solutions to the Linearized Boltzmann Equations