Phi-entropy inequalities and Fokker-Planck equations

François Bolley (1) , Ivan Gentil (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We present new $\Phi$-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.

Mots clés: Logarithmic Sobolev inequality; Poincaré inequality; $\Phi$-entropies; Bakry-Emery criterion; diffusion semigroups; Fokker-Planck equation

Domaines: Probabilités [math.PR]

François Bolley, Ivan Gentil. Phi-entropy inequalities and Fokker-Planck equations. 2010, pp.7. ⟨10.1142/9789814313179_0060⟩. ⟨hal-00459423⟩