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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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