Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
arXiv:2411.13788 · doi:10.1515/forum-2023-0413
Abstract
In this paper, we obtain the reverse Bakry-Émery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré 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.
Modify minor errors after acceptance by Forum Math