Duality on gradient estimates and Wasserstein controls

Details Duality on gradient estimates and Wasserstein controls Duality on gradient estimates and Wasserstein controls

2009-10-09

arxiv.org/abs/0910.1741v1

Mathematics

Probability

Scientific paper

We establish a duality between L^p-Wasserstein control and L^q-gradient estimate in a general framework. Our result extends a known result for a heat flow on a Riemannian manifold. Especially, we can derive a Wasserstein control of a heat flow directly from the corresponding gradient estimate of the heat semigroup without using any other notion of lower curvature bound. By applying our result to a subelliptic heat flow on a Lie group, we obtain a coupling of heat distributions which carries a good control of their relative distance.

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