Abstract

CECCON, Jurandir  and  MONTENEGRO, Marcos. General optimal euclidean Sobolev and Gagliardo-Nirenberg inequalities. An. Acad. Bras. Ciênc. [online]. 2005, vol.77, n.4, pp. 581-587. ISSN 0001-3765.  http://dx.doi.org/10.1590/S0001-37652005000400001.

We prove general optimal euclidean Sobolev and Gagliardo-Nirenberg inequalities by using mass transportation and convex analysis results. Explicit extremals and the computation of some optimal constants are also provided. In particular we extend the optimal Gagliardo-Nirenberg inequality proved by Del Pino and Dolbeault 2003 and the optimal inequalities proved by Cordero-Erausquin et al. 2004.

Keywords : best constants; Gagliardo-Nirenberg inequalities; mass transportation; convex analysis.