We give two direct proofs of Sobolev estimates for the positive part of Boltzmanns kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.
Cite this article
François Bouchut, Laurent Desvillettes, A proof of the smoothing properties of the positive part of Boltzmann's kernel. Rev. Mat. Iberoam. 14 (1998), no. 1, pp. 47–61