Functional Inequalities for Markov semigroups

By D. Bakry. 2009

113 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/89a97e43a93776f7194b743b683f76d866d6f598

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Citations in the corpus

The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds (2008, background): “From the point of view of partial differential equations (see [4], [18]), gradient estimates had proved to be a very efficient tool for the control of the rate of convergence to equilibrium, quantitative estimates on the regularization properties of heat kernels, functional inequalities such as Poin”
Convergence rates for rank-based models with applications to portfolio theory (2011, background): “1 in the notes by Bakry [2]) that a Poincaré inequality as proved in Lemma 7 implies that for any function f ∈ L(2)(G; ρ) such that ∫ G f(x)ρ(x)dx = 0 one has”
On the differential structure of metric measure spaces and applications (2012, background): “The regularity result |Dg|w ∈ W (1,2)(X, d,m) is non-trivial and follows from a generalization of works of Barky in the context of Dirichlet forms [9]”
Phi-entropy inequalities for diffusion semigroups (2008, methodology): “semigroup or generator is called a diffusion, and we refer to [Bak94], [Led00] or [ Bak06 ] for backgrounds on these semigroups.”
A formula for the time derivative of the entropic cost and applications (2019, unknown): “Secondly, Pt enjoys an L ∞-Lipschitz regularization (see [4]), namely for all u ∈ L∞(m) it holds ‖∇Ptu‖L∞(m) ≤ 1 √ 2I2κ(t) ‖u‖L∞(m) with Iκ(t) := exp(κt) − 1 κ , ∀t > 0.”
Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries (2011, background): “2) does provide sharp geometric constants (see [6], [36]).”
On the Bakry-\'Emery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces (2013, unknown): “approach [9], see also [8,10], uses the formalism of Dirichlet forms (and the heat flow associated with the Dirichlet form) and is based on the so-called BE(K , N ) condition, formally expressed in differential terms by”
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure (2012, background): “2), which can be proven following the Γ-calculus tools of Bakry [8], see Theorem 6.”
Metric measure spaces with Riemannian Ricci curvature bounded from below (2011, methodology): “We conclude this section with an example of application, following the ideas of [5], of the calculus tools developed in Section 4.”
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds (2012, methodology): “The Bakry-Émery condition BE(K,∞) can then be stated in a weak integral form (strongly inspired by [11, 15, 57]) just involving the Markov semigroup (Pt)t≥0 (see (2.”
A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality (2010, background): “1 we remark that it constitutes a generalization of the so-called curvature-dimension inequality CD(ρ1, n) from Riemannian geometry, see [BE], [Ba], [St1], [St2], [LV].”