Regularity of stationary solutions to the linearized Boltzmann equations

I-Kun Chen

Published 2016-04-13Version 1

We consider the regularity of the solutions to the stationary 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 functional space for existence results for boundary value problems. We prove that this solution is H\"older continuous with order $\frac1{3}^-$ away from the boundary provided the incoming data has the same regularity and uniformly bounded by a fixed function in velocity with finite weighted $L^2$ norm with the weight of collision frequency. The key idea is to partially transfer the regularity in velocity obtained by the integral part of the collision operator to the space through transport and collision.