Sobolev and Hardy-Littlewood-Sobolev inequalities

Jean Dolbeault (1) , Gaspard Jankowiak (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

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

Domaines: Equations aux dérivées partielles [math.AP]

Jean Dolbeault, Gaspard Jankowiak. Sobolev and Hardy-Littlewood-Sobolev inequalities. 2014. ⟨hal-00915998v2⟩