Sobolev and Hardy-Littlewood-Sobolev inequalities - Archive ouverte HAL Access content directly
Journal Articles Journal of Differential Equations Year : 2014

Sobolev and Hardy-Littlewood-Sobolev inequalities

Abstract

This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities. Then we focus our attention on the constants in our improved Sobolev inequalities, that can be estimated by completion of the square methods. Our estimates rely on nonlinear flows and spectral problems based on a linearization around optimal Aubin-Talenti functions.
Fichier principal
Vignette du fichier
DJ2014Final-Hal.pdf (312.23 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00915998 , version 1 (09-12-2013)
hal-00915998 , version 2 (01-02-2014)
hal-00915998 , version 3 (30-04-2014)

Identifiers

Cite

Jean Dolbeault, Gaspard Jankowiak. Sobolev and Hardy-Littlewood-Sobolev inequalities. Journal of Differential Equations, 2014, 257 (6), pp.1689-1720. ⟨hal-00915998v3⟩
697 View
1975 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More