Hypoelliptic Regularity in Kinetic Equations

By F. De. 2003

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Regularity of Stochastic Kinetic Equations (2016, methodology): “Such result requires basic L-estimates proved in [4] and [5] and non-standard interpolation techniques for functions from R with values in Bessel-Sobolev spaces (see in particular the proofs of Theorem 3.”
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, methodology): “More recently, Bouchut [7] has obtained more quantitative Sobolev regularity estimates.”
The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels (2004, background): “Besides, it has been previously noticed in various contexts that the velocity averaging method combined with additional regularity estimates in the velocity variable only gives compactness in all variables: see for instance [48], [22], and [13].”
Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation (2009, result): “Some results on similar but linear kinetic equations were also given in [9] and [18].”
A real space method for averaging lemmas (2004, background): “It was noticed recently in [4], that the operator v r x has some regularizing e ects of its own.”