The Harnack inequality fails for nonlocal kinetic equations
Analysis of PDEs
2024-11-05 v2 Probability
Abstract
We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest equation in this theory, the fractional Kolmogorov equation. Our result reflects a purely nonlocal phenomenon since the Harnack inequality holds true for local kinetic equations like the Kolmogorov equation.
Keywords
Cite
@article{arxiv.2405.05223,
title = {The Harnack inequality fails for nonlocal kinetic equations},
author = {Moritz Kassmann and Marvin Weidner},
journal= {arXiv preprint arXiv:2405.05223},
year = {2024}
}
Comments
to appear in Adv. Math