Duality on gradient estimates and Wasserstein controls

作者：Kuwada Kazumasa^*

来源：Journal of Functional Analysis, 2010, 258(11): 3758-3774.

DOI：10.1016/j.jfa.2010.01.010

• Wasserstein distance
• Gradient estimate
• Subelliptic diffusion
• Hamilton-Jacobi semigroup

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.

• 出版日期2010-6-1