Fractional order kinetic equations and hypoellipticity

TL;DR

This paper provides straightforward proofs of hypoelliptic estimates for kinetic equations with fractional diffusion, enhancing understanding of their regularity properties using energy methods inspired by prior research.

Contribution

It introduces simplified proof techniques for hypoelliptic estimates in fractional kinetic equations, building on and streamlining previous approaches.

Findings

Established hypoelliptic estimates for fractional kinetic models

Demonstrated the effectiveness of energy-based proof methods

Connected fractional diffusion with hypoelliptic regularity

Abstract

We give simple proofs of hypoelliptic estimates for some models of kinetic equations with a fractional order diffusion part. The proofs are based on energy estimates together with F. Bouchut and B. Perthame previous ideas.