Duality on gradient estimates and Wasserstein controls

Kazumasa Kuwada

Research output: Contribution to journalArticlepeer-review

57 Citations (Scopus)


We establish a duality between Lp-Wasserstein control and Lq-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.

Original languageEnglish
Pages (from-to)3758-3774
Number of pages17
JournalJournal of Functional Analysis
Issue number11
Publication statusPublished - 2010 Jun 1


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

ASJC Scopus subject areas

  • Analysis


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