A note on some Poincaré inequalities on convex sets by Optimal Transport methods

Lorenzo Brasco (1, 2) , Filippo Santambrogio (3)

1 Department of Mathematics [Ferrara]
2 I2M - Institut de Mathématiques de Marseille
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We show that a class of Poincaré-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly unbounded.

Mots clés: Poincaré inequalities; Wasserstein distances

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

Lorenzo Brasco, Filippo Santambrogio. A note on some Poincaré inequalities on convex sets by Optimal Transport methods. 2015. ⟨hal-01249425⟩