Hypoelliptic estimates for some linear diffusive kinetic equations
Journées équations aux dérivées partielles (2010), article no. 9, 13 p.

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.

DOI: 10.5802/jedp.66
Classification: 35H10,  35H20,  35B65,  82C40
Keywords: Kinetic equations, Regularity, global hypoelliptic estimates, hypoellipticity, anisotropic diffusion, Wick quantization, Landau, Fokker-Planck
Hérau, Frédéric 1

1 Laboratoire de Mathématiques Jean Leray 2, rue de la Houssinière - BP 92208 F-44322 Nantes Cedex 3
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     title = {Hypoelliptic estimates for some linear diffusive kinetic equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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Hérau, Frédéric. Hypoelliptic estimates for some linear diffusive kinetic equations. Journées équations aux dérivées partielles (2010), article  no. 9, 13 p. doi : 10.5802/jedp.66. http://archive.numdam.org/articles/10.5802/jedp.66/

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