Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

TL;DR

This paper establishes global subelliptic estimates for the linearized Boltzmann operator without angular cutoff, revealing a gain in spatial regularity despite the operator's non-ellipticity, using advanced symbolic analysis techniques.

Contribution

It introduces novel global subelliptic estimates for the Boltzmann operator without angular cutoff, employing multiplier methods and Wick quantization for the first time in this context.

Findings

Proves global subelliptic estimates for the operator

Shows spatial regularity gain despite non-ellipticity

Utilizes symbolic analysis of the Weyl symbol

Abstract

In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbolic properties of the Weyl symbol of the Boltzmann collision operator.