Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
Probability
2024-11-22 v1
Abstract
In this paper, we obtain the reverse Bakry-\'Emery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincar\'e inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang-Harnack inequality, Hamilton's gradient estimate and Liouville property are also presented by reverse logarithmic Sobolev inequality.
Keywords
Cite
@article{arxiv.2411.13788,
title = {Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling},
author = {Bin Qian and Beibei Zhang},
journal= {arXiv preprint arXiv:2411.13788},
year = {2024}
}
Comments
Modify minor errors after acceptance by Forum Math