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Detailed view Article in peer-reviewed journal
Annales de l'Institut Henri Poincaré Analyse non linéaire 22 (2005) 127-142
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About $L^p$ estimates for the spatially homogeneous Boltzmann equation
Laurent Desvillettes1, Clément Mouhot2

For the homogeneous Boltzmann equation with (cutoff or non cutoff ) hard potentials, we prove estimates of propagation of Lp norms with a weight $(1+ |x|^2)^q/2$ ($1 < p < +\infty$, $q \in \R_+$ large enough), as well as appearance of such weights. The proof is based on some new functional inequalities for the collision operator, proven by elementary means.
1:  CMLA - Centre de Mathématiques et de Leurs Applications
2:  CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
Boltzmann equation – spatially homogeneous – non-cutoff – integrability estimates