Abstract
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 language | English |
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Pages (from-to) | 3758-3774 |
Number of pages | 17 |
Journal | Journal of Functional Analysis |
Volume | 258 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2010 Jun 1 |
Keywords
- Gradient estimate
- Hamilton-Jacobi semigroup
- Subelliptic diffusion
- Wasserstein distance
ASJC Scopus subject areas
- Analysis