TY - JOUR
T1 - Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates
AU - Kuwada, Kazumasa
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/9/20
Y1 - 2015/9/20
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-014-0781-2
DO - 10.1007/s00526-014-0781-2
M3 - Article
AN - SCOPUS:84939465717
VL - 54
SP - 127
EP - 161
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
ER -