Asymptotic expansions and extremals for the critical Sobolev and Gagliardo- Nirenberg inequalities on a torus

被引：14

作者：

Bartuccelli, Michele ^{[1
]}

Deane, Jonathan ^{[1
]}

Zelik, Sergey ^{[1
]}

机构：

[1] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2013年 / 143卷 / 03期

关键词：

WAINGER TYPE INEQUALITY; SHARP CONSTANTS; EQUATION;

D O I：

10.1017/S0308210511000473

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms, etc. Most attention is paid to the critical (logarithmic) Sobolev inequality in the two-dimensional case, although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained.

引用

页码：445 / 482

页数：38

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