• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

The Moser-Trudinger-Onofri inequality

Thumbnail
Date
2015
Link to item file
https://arxiv.org/abs/1403.5042v3
Dewey
Analyse
Sujet
Moser-Trudinger-Onofri inequality; Duality; Mass transportation; Fast diffusion equation; Rigidity
Journal issue
Chinese Annals of Mathematics. Series B
Volume
36
Number
5
Publication date
2015
Article pages
777-802
Publisher
Shanghai Scientific and Technological Literature Publishing House
DOI
http://dx.doi.org/10.1007/s11401-015-0976-7
URI
https://basepub.dauphine.fr/handle/123456789/13034
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Dolbeault, Jean
Esteban, Maria J.
Jankowiak, Gaspard
Type
Article accepté pour publication ou publié
Abstract (EN)
This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, we state several elementary remarks. We also prove various new results. We give a proof of the inequality using mass transportation methods (in the radial case), consistently with similar results for Sobolev's inequalities. We investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality. In the framework of fast diffusion equations, we establish that the inequality is an entropy--entropy production inequality, which provides an integral remainder term. Finally we give a proof of the inequality based on rigidity methods and introduce a related nonlinear flow.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.