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Journées équations aux dérivées partielles

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Frédéric Hérau
Hypoelliptic estimates for some linear diffusive kinetic equations
Journées équations aux dérivées partielles (2010), Exp. No. 9, 13 p., doi: 10.5802/jedp.66
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Class. Math.: 35H10, 35H20, 35B65, 82C40
Mots clés: Kinetic equations, Regularity, global hypoelliptic estimates, hypoellipticity, anisotropic diffusion, Wick quantization, Landau, Fokker-Planck

Résumé - Abstract

This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations, we establish optimal global hypoelliptic estimates with loss of $4/3$ derivatives in a Sobolev scale exactly related to the anisotropy of the diffusion.

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