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arXiv · 0812.0800

Phi-entropy inequalities for diffusion semigroups

François Bolley·Ivan Gentil
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Abstract

We obtain and study new $Φ$-entropy inequalities for diffusion semigroups, with Poincaré 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 $Γ_2$ criterion of D. Bakry and M. Emery appears as a main tool in the analysis, in local or integral forms.

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François Bolley, Ivan Gentil. 2010-01-05. Phi-entropy inequalities for diffusion semigroups. https://arxiv.org/abs/0812.0800

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