Uniqueness theorems for the linearized Boltzmann equation

Two theorems are proved about the solutions of the linearized Boltzmann equation with Maxwell boundary conditions. First, it is shown that the solution of the initial value problem is unique. Then, it is shown that the solution of the time-independent boundary-value problem is unique up to an additive constant. It can be made completely unique by adding a simple additional condition. The only essential property used in the proofs are the negative semidefinite character of the collision operator. The mathematics used are just Gauss theorem and Schwarz' inequality.