Global hypoelliptic estimates for a linear model of non-cutoff Boltzmann equation

TL;DR

This paper establishes optimal global hypoelliptic estimates with weights for a linear model of the non-cutoff Boltzmann equation, advancing understanding of its regularity properties.

Contribution

It applies the multiplier method to derive the first optimal global hypoelliptic estimates for this class of linear Boltzmann models without angular cutoff.

Findings

Proves optimal hypoelliptic estimates with weights

Extends multiplier method to non-cutoff Boltzmann models

Provides a foundation for further regularity analysis

Abstract

In this paper we study a linear model of spatially inhomogeneous Boltzmann equation without angular cutoff. Using the multiplier method introduced by F. H\'{e}rau and K. Pravda-Starov (2011), we establish the optimal global hypoelliptic estimate with weights for the linear model operator