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On heat kernel logarithmic Sobolev inequalities. (English) Zbl 0918.60039

Davies, I. M. (ed.) et al., Stochastic analysis and applications. Proceedings of the 5th Gregynog symposium, Gregynog, Powys, GB, July 9-14, 1995. Singapore: World Scientific. 189-200 (1996).
Summary: This note is devoted to a pedagogical proof of logarithmic Sobolev inequalities on compact Riemannian manifolds when the reference measure is taken to be a heat kernel measure. The inequalities explained in this paper seem to have been first discovered by D. Bakry and M. Ledoux [Private communication in Nov. 1994 at the Taniguchi Symp., held in England].
For the entire collection see [Zbl 0901.00050].

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
47J20 Variational and other types of inequalities involving nonlinear operators (general)
58J35 Heat and other parabolic equation methods for PDEs on manifolds
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