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arXiv · 2411.13788

Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling

Bin Qian·Beibei Zhang
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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.

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Bin Qian, Beibei Zhang. 2024-11-21. Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling. https://doi.org/10.1515/forum-2023-0413

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