Anisotropic hypoelliptic estimates for Landau-type operators

✍ Scribed by F. Hérau; K. Pravda-Starov

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 325 KB
• Volume: 95
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2010.11.003

✦ Synopsis

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.