Phi-entropy inequalities for diffusion semigroups
نویسندگان
چکیده
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 Γ2 criterion of D. Bakry and M. Emery appears as a main tool in the analysis, in local or integral forms.
منابع مشابه
Phi-entropy inequalities and Fokker-Planck equations
We present new Φ-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.
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