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arXiv · 1003.3265

Anisotropic hypoelliptic estimates for Landau-type operators

Frederic Herau·Karel Pravda-Starov
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Abstract

We establish global hypoelliptic estimates for 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 for linear Landau-type operators optimal global hypoelliptic estimates with loss of 4/3 derivatives in a Sobolev scale which is exactly related to the anisotropy of the diffusion.

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Frederic Herau, Karel Pravda-Starov. 2010-03-16. Anisotropic hypoelliptic estimates for Landau-type operators. https://arxiv.org/abs/1003.3265

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