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Gradient estimates on manifolds using coupling. (English) Zbl 0770.58038
Using a probabilistic coupling technique on a complete Riemannian manifold $$M$$, an estimate is given for the gradient of solutions to $$(1/2\Delta+Z)u=0$$. Here $$\Delta$$ is the Laplacian and $$Z$$ a given vector field. The bound in the gradient estimate depends on the bounds of $$Z$$ and on a lower bound on the Ricci curvature of $$M$$.

##### MSC:
 58J05 Elliptic equations on manifolds, general theory 58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) 60G46 Martingales and classical analysis
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##### References:
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