On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain

Abstract

In this article, we study the stationary Boltzmann equation with the incoming boundary condition for the hard potential cases. Assuming the smallness of the domain and a suitable normal curvature condition on the boundary, we find a suitable solution space which is a proper subset of the $W^{1,p}$ space for $1\le p<3$.