The duality in Bakry–Émery’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 L2-Wasserstein control for heat distributions at different times. The Lp-version of those estimates are studied on Riemannian manifolds via coupling method.
|Number of pages||35|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2015 Sep 20|
ASJC Scopus subject areas
- Applied Mathematics