A new proof of the transfer of regularity for kinetic equations

TL;DR

This paper introduces a novel trajectory-based method for transfer-of-regularity estimates in kinetic equations, avoiding Fourier computations and fundamental solutions, while achieving sharp, scale-invariant results.

Contribution

The paper presents a new approach that simplifies transfer-of-regularity proofs for kinetic equations without Fourier analysis or fundamental solutions.

Findings

Achieves sharp, scale-invariant homogeneous estimates.

Avoids explicit Fourier variable computations.

Provides a new trajectory-based proof technique.

Abstract

We present a new trajectory-based approach to transfer-of-regularity estimates \`a la Bouchut-H\"ormander for kinetic equations at the weak scale of local diffusion. The method avoids explicit computations in Fourier variables and does not rely on the fundamental solution, while still yielding sharp, scale-invariant homogeneous estimates.