Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis
by Marc Arnaudon and Anton Thalmaier

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.

Advanced Studies in Pure Mathematics 57 (2010) 29-48

The paper is available here:

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Marc Arnaudon
Anton Thalmaier

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