eprintid: 26149
rev_number: 11
eprint_status: archive
userid: 1482
importid: 105
dir: disk0/00/02/61/49
datestamp: 2018-07-25 07:42:35
lastmod: 2024-04-17 06:15:55
status_changed: 2018-07-25 07:42:35
type: monograph
metadata_visibility: show
creators_name: Blanchet, Adrien
creators_name: Bolte, Jérôme
creators_idrefppn: 12046246X
creators_idrefppn: 078638623
title: A family of functional inequalities
ispublished: pub
subjects: subjects_ECO
abstract: 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.
date: 2017-03
date_type: published
publisher: IAST Working Paper
official_url: http://iast.fr/pub/31597
sub_title: lojasiewicz inequalities and displacement convex functions
faculty: tse
divisions: tse
language: en
has_fulltext: TRUE
view_date_year: 2017
full_text_status: public
monograph_type: working_paper
series: IAST Working Paper
volume: 17-66
place_of_pub: Toulouse
pages: 11
institution: Université Toulouse 1 Capitole
department: Toulouse School of Economics
book_title: IAST Working Paper
oai_identifier: oai:tse-fr.eu:31597
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harvester_local_overwrite: faculty
harvester_local_overwrite: institution
harvester_local_overwrite: place_of_pub
harvester_local_overwrite: pages
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oai_lastmod: 2024-04-16T12:30:58Z
oai_set: tse
site: ut1
citation:   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     
document_url: https://publications.ut-capitole.fr/id/eprint/26149/1/IAST_V1/wp/wp_iast_1766.pdf