We present an study of the integrability properties of a more general version of the Boltzmann collision operator that includes inelastic interactions between particles. We will show proofs of a Young’s inequality estimate for the case of hard potentials, a Hardy-Littlewood-Sobolev inequality estimate for soft potentials, and an estimate with Maxwellian weights for hard potentials. The main technique used to derive the results is the radial average symmetrization.
Copyright. All Rights Reserved.