JournalsrmiVol. 14, No. 1pp. 47–61

A proof of the smoothing properties of the positive part of Boltzmann's kernel

  • François Bouchut

    Ecole Normale Superieure, Paris, France
  • Laurent Desvillettes

    CMLA-ENS, Cachan, France
A proof of the smoothing properties of the positive part of Boltzmann's kernel cover
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Abstract

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

DOI 10.4171/RMI/233