A COMPACTNESS RESULT RELATED TO THE STATIONARY BOLTZMANN-EQUATION IN A SLAB, WITH APPLICATIONS TO THE EXISTENCE THEORY

Weak compactness in L(1)([a, b] x R(3)) is proved for any sequence of functions for which a weighted L(1)-norm and the Boltzmann entropy pro duction term are bounded, and which satisfy some very weak condition o f local boundedness from below. The property holds for a wide class of collision kernels. This result is then used to solve the stationary B oltzmann equation in a slab, for given indata and for diffuse reflecti on with total inflow given under various small velocity truncations of the collision kernel.