Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations

TL;DR

This paper establishes boundedness estimates for weak solutions to a broad class of nonlinear nonlocal kinetic equations, highlighting the role of nonlocal diffusion contributions in local regularity.

Contribution

It introduces an interpolative a priori boundedness estimate for weak subsolutions, accounting for nonlocal diffusion effects in nonlinear kinetic equations.

Findings

Proved boundedness estimates involving tail terms for nonlocal kinetic equations.

Extended regularity theory to a broad class of nonlinear nonlocal operators.

Provided tools for analyzing local behavior of solutions with nonlocal influences.

Abstract

We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving an interpolative apriori boundedness estimate for weak subsolutions in terms of a tail term encoding the nonlocal contributions of the diffusion.