A Proof of the Smoothing Properties of the Positive Part of Boltzmann's Kernel
نویسنده
چکیده
We give two direct proofs of Sobolev estimates for the positive part of Boltzmann's kernel. The rst 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. R esum e. Nous donnons deux preuves directes des estimations de Sobolev pour la partie positive du noyau de Boltzmann. La premi ere concerne les sections e caces a variables s epar ees; aucune d eriv ee n'est n ecessaire dans ce cas. La deuxi eme traite des sections e caces g en erales ayant une d eriv ee dans la variable angulaire.
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