On the Existence of $H^1$ solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

Abstract

In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in $\Omega \subseteq {\mathbb{R}}^3$. For a $C^2$ bounded domain with boundary of positive Gaussian curvature, the existence theory is established in $H^1(\Omega \times {\mathbb{R}}^3)$ provided that the diameter of the domain $\Omega$ is small enough.

19 pages, 1 figure