General optimal euclidean Sobolev and Gagliardo-Nirenberg inequalities

Anais da Academia Brasileira de Ciências

Jurandir Ceccon¹  Marcos Montenegro¹ 

[1] ,Universidade Federal de Minas Gerais Departamento de Matemática - ICEx Belo Horizonte MG ,Brasil

关键词: best constants;    Gagliardo-Nirenberg inequalities;    mass transportation;    convex analysis;    melhores constantes;    desigualdades de Gagliardo-Nirenberg;    transporte de massa;    análise convexa;   

DOI  :  10.1590/S0001-37652005000400001

来源: SciELO

【 摘 要 】

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.

【 授权许可】

CC BY   
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