Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis

Details Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis

2009-02-16

arxiv.org/abs/0902.2681v1

Mathematics

Probability

Scientific paper

In this paper we use methods from Stochastic Analysis to establish Li-Yau type estimates for positive solutions of the heat equation. In particular, we want to emphasize that Stochastic Analysis provides natural tools to derive local estimates in the sense that the gradient bound at given point depends only on universal constants and the geometry of the Riemannian manifold locally about this point.

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