Sobolev and Hardy-Littlewood-Sobolev inequalities

Jankowiak, Gaspard; Dolbeault, Jean

Jankowiak, Gaspard; Dolbeault, Jean (2014), Sobolev and Hardy-Littlewood-Sobolev inequalities, Journal of Differential Equations, 257, 6, p. 1689–1720. http://dx.doi.org/10.1016/j.jde.2014.04.021

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00915998

Date

2014

Journal name

Journal of Differential Equations

Volume

257

Number

Publisher

Elsevier

Pages

1689–1720

Abstract (EN)

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. We focus our attention on optimal constants, that can be achieved either by completion of the square methods or by using nonlinear flows, and provide various new estimates.

Subjects / Keywords

fast diffusion equation; stereographic projection; best constants; duality; extremal functions; Caffarelli-Kohn-Nirenberg inequalities; Onofri's inequality; logarithmic Hardy-Littlewood-Sobolev inequality; Hardy-Littlewood-Sobolev inequality; Sobolev inequality; Sobolev spaces