English

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