Functional Inequalities for Markov semigroups

Dominique Bakry (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In these notes, we describe some of the most interesting inequalities related to Markov semigroups, namely spectral gap inequalities, Logarithmic Sobolev inequalities and Sobolev inequalities. We show different aspects of their meanings and applications, and then describe some tools used to establish them in various situations.

Mots clés: Markov semigroups; Logarithmic Sobolev inequalities; evolution equations

Domaines: Analyse fonctionnelle [math.FA]; Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Dominique Bakry. Functional Inequalities for Markov semigroups. Probability measures on groups, 2004, Mumbai, India. pp.91-147. ⟨hal-00353724⟩