Global subelliptic estimates for Kramers-Fokker-Planck operators with some class of polynomials

TL;DR

This paper establishes global subelliptic estimates for a class of Kramers-Fokker-Planck operators with polynomial potentials of degree greater than two, extending understanding of their regularity properties.

Contribution

It provides the first accurate global subelliptic estimates for KFP operators with polynomial potentials of degree greater than two under specific conditions.

Findings

Established global subelliptic estimates for KFP operators with polynomial potentials

Extended regularity results to potentials with degree > 2

Provided conditions under which estimates hold

Abstract

In this article we study some Kramers-Fokker-Planck operators with a polynomial potential $V(q)$ of degree greater than two having quadratic limiting behavior. This work provides an accurate global subelliptic estimate for KFP operators under some conditions imposed on the potential.