On estimates of solutions of Fokker--Planck--Kolmogorov equations with potential terms and non uniformly elliptic diffusion matrices

TL;DR

This paper derives upper bounds and new estimates for solutions of Fokker-Planck-Kolmogorov equations with unbounded coefficients and non-uniformly elliptic diffusion matrices, using Lyapunov functions.

Contribution

It introduces novel estimates involving Lyapunov functions for Fokker-Planck-Kolmogorov equations with unbounded coefficients and non-uniform ellipticity.

Findings

Established upper estimates for solutions.

Developed new Lyapunov-based estimates.

Addressed equations with unbounded coefficients.

Abstract

We consider Fokker--Planck--Kolmogorov equations with unbounded coefficients and obtain upper estimates of solutions. We also obtain new estimates involving Lyapunov functions.