TY - JOUR
T1 - Duality on gradient estimates and Wasserstein controls
AU - Kuwada, Kazumasa
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010/6/1
Y1 - 2010/6/1
N2 - 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.
AB - 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.
KW - Gradient estimate
KW - Hamilton-Jacobi semigroup
KW - Subelliptic diffusion
KW - Wasserstein distance
UR - http://www.scopus.com/inward/record.url?scp=77949569321&partnerID=8YFLogxK
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U2 - 10.1016/j.jfa.2010.01.010
DO - 10.1016/j.jfa.2010.01.010
M3 - Article
AN - SCOPUS:77949569321
VL - 258
SP - 3758
EP - 3774
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 11
ER -