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

Kazumasa Kuwada

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)127-161
Number of pages35
JournalCalculus of Variations and Partial Differential Equations
Issue number1
Publication statusPublished - 2015 Sep 20
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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