Regularity of kinetic Fokker-Planck equations in bounded domains

TL;DR

This paper establishes existence, uniqueness, and regularity of solutions to kinetic Fokker-Planck equations with various boundary conditions in bounded domains, advancing mathematical understanding of these equations.

Contribution

It provides new regularity results for kinetic Fokker-Planck equations with measurable coefficients and different boundary conditions, which was previously less understood.

Findings

Existence and uniqueness of solutions proven.

Regularity results established for solutions.

Applicable to multiple boundary conditions.

Abstract

We obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditions, including the inflow, diffuse reflection and specular reflection cases.