Sobolev and Hardy-Littlewood-Sobolev inequalities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Dolbeault, Jean¹  Jankowiak, Gaspard¹ 

[1] Univ Paris 09, CEREMADE, F-75775 Paris, France

关键词: Sobolev inequality;    Hardy-Littlewood-Sobolev inequality;    Onofri's inequality;    Duality;    Fast diffusion equation;    Best constants;   

DOI  :  10.1016/j.jde.2014.04.021

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free