relation: https://publications.ut-capitole.fr/id/eprint/26149/
title: A family of functional inequalities
creator: Blanchet, Adrien
creator: Bolte, Jérôme
subject: B- ECONOMIE ET FINANCE
description: For displacement convex functionals in the probability space equipped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Lojasiewicz inequalities. In a second part, we specialise these inequalities to some classical geodesically convex functionals. For the Boltzmann entropy, we obtain the equivalence between logarithmic Sobolev and Talagrand's inequalities. On the other hand, the non-linear entropy and the Gagliardo-Nirenberg inequality provide a Talagrand inequality which seems to be a new equivalence. Our method allows also to recover some results on the asymptotic behaviour of the associated gradient flows.
publisher: IAST Working Paper
date: 2017-03
type: Monograph
type: NonPeerReviewed
format: text
language: en
identifier: https://publications.ut-capitole.fr/id/eprint/26149/1/IAST_V1/wp/wp_iast_1766.pdf
identifier:   Blanchet, Adrien <https://www.idref.fr/12046246X> and Bolte, Jérôme <https://www.idref.fr/078638623>  (2017)  A family of functional inequalities: lojasiewicz inequalities and displacement convex functions. IAST Working Paper, n. 17-66, Toulouse     
relation: http://iast.fr/pub/31597
language: en