General optimal euclidean Sobolev and Gagliardo-Nirenberg inequalities.
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.
Ceccon
Jurandir
J
Departamento de Matemática, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970 Belo Horizonte, MG, Brazil.
Montenegro
Marcos
M