Anisotropic hypoelliptic estimates for Landau-type operators

作者：Herau F^*; Pravda Starov K

来源：Journal de Mathematiques Pures et Appliquees, 2011, 95(5): 513-552.

DOI：10.1016/j.matpur.2010.11.003

• Kinetic equations
• Landau equation
• Fokker-Planck equation
• Hypoellipticity
• Anisotropic diffusion
• Wick quantization

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 linear inhomogeneous 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.

• 出版日期2011-5