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Probability Versions of Li-Yau Type Inequalities and Applications by Wang, Feng-Yu; Cheng, Li-Juan is a scholarly article available to read on EtoBox.

What is Probability Versions of Li-Yau Type Inequalities and Applications about?

By using stochastic analysis, two probability versions of Li-Yau type inequalities are established for diffusion semigroups on a manifold possibly with (non-convex) boundary. The inequalities are explicitly given by the Bakry-Emery curvature-dimension, as well as the lower bound of the second fundamental form if the boundary exists. As applications, a number of global and local estimates are presented, which extend or improve existing ones derived for manifolds without boundary. Compared with the maximum principle technique developed in the literature, the probabilistic argument we used is more straightforward and hence considerably simpler.

Author

Wang, Feng-Yu; Cheng, Li-Juan

Published

2024

Language

EN