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Hypoelliptic and spectral estimates for some linear operators of Landau type

Mohamad Rachid

Vol. 5 (2023), No. 1, 1–46
Abstract

We establish hypoelliptic estimates, a localization of the spectrum and the estimates of the resolvent for general operators of Landau type. The proof is based on a multiplier method and relies on an accurate parameter-dependent relationship between Weyl and anti-Wick calculus. Moreover, we apply these results to the true linearized inhomogeneous Landau equation.

Keywords
kinetic theory, Landau equation, pseudospectrum, hypoellipticity, Wick quantization
Mathematical Subject Classification
Primary: 47A10 , 47A11, 47G30
Milestones
Received: 24 January 2021
Revised: 6 June 2022
Accepted: 24 July 2022
Published: 24 April 2023
Authors
Mohamad Rachid
CERMICS
École des Ponts ParisTech
Marne-La-Vallée
France