Existence of solutions to the stationary linear Boltzmann equation

This article considers the stationary linear Boltzmann equation in a convex bounded domain with Cl-boundary, and at the ingoing boundary, either with given indata, diffuse reflection or a combination of both. First, a unique weak P-solution is constructed in the case with combined indata, and boundedness of its higher moments is established. Then under some restrictions on the collision operator, the existence of a weak L-1-solution is proved for the case of pure diffuse reflection.