Phi-entropy inequalities for diffusion semigroups
By Franccois Bolley, Ivan Gentil. 2008
63 citations recorded by the source corpus.
We obtain and study new $\Phi$-entropy inequalities for diffusion semigroups, with Poincare or logarithmic Sobolev inequalities as particular cases. From this study we derive the asymptotic behaviour of a large class of linear Fokker-Plank type equations under simple conditions, widely extending previous results. Nonlinear diffusion equations are also studied by means of these inequalities. The $\Gamma_2$ criterion of D.~Bakry and M. Emery appears as a main tool in the analysis, in local or integral forms.
View Paper: https://www.semanticscholar.org/paper/19fd1d158196fc71aeb03b9df20cf77e8a1e33c7
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Citations in the corpus
- Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations (2016, unknown): “, [1], [2], [16], [17], [18], [20], [21], [23], [30], and [33].”
- Nonlinear flows and rigidity results on compact manifolds (2013, background): “Inequality (3) has been studied for p ∈ (1, 2) and various probability measures, mostly defined on the Euclidean space: we may refer for instance to [9, 10, 45, 30, 35, 22].”