Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates

作者：Kuwada Kazumasa^*

来源：Calculus of Variations and Partial Differential Equations, 2015, 54(1): 127-161.

DOI：10.1007/s00526-014-0781-2

The duality in Bakry-A parts per thousand mery's gradient estimates and Wasserstein controls for heat distributions is extended to that in refined estimates in a high generality. As a result, we find an equivalent condition to Bakry-Ledoux's refined gradient estimate involving an upper dimension bound. This new condition is described as a -Wasserstein control for heat distributions at different times. The -version of those estimates are studied on Riemannian manifolds via coupling method.

• 出版日期2015-9