Nash's $G$ bound for the Kolmogorov equation
Analysis of PDEs
2025-10-27 v1
Abstract
We prove Nash's bound for the Kolmogorov equation with rough coefficients. Our proof is inspired by the treatment of the parabolic problem by Nash (1958) and Fabes and Stroock (1986). To transfer their ideas to the kinetic setting, we employ critical kinetic trajectories. From Nash's bound, we recover the sharp lower bound on the fundamental solution and thus provide an alternative proof of the Harnack inequality for the Kolmogorov equation.
Keywords
Cite
@article{arxiv.2510.21621,
title = {Nash's $G$ bound for the Kolmogorov equation},
author = {Helge Dietert and Lukas Niebel},
journal= {arXiv preprint arXiv:2510.21621},
year = {2025}
}