About $L^p$ estimates for the spatially homogeneous Boltzmann equation
Résumé
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.
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