Best constants in Sobolev inequalities on Riemannian manifolds in the presence of symmetries

被引：19

作者：

Faget, Z ^{[1
]}

机构：

[1] Univ Paris 06, Inst Math, Equipe Geometrie & Dynam, F-75013 Paris, France

来源：

POTENTIAL ANALYSIS | 2002年 / 17卷 / 02期

关键词：

best constants; Sobolev inequalities; isometries;

D O I：

10.1023/A:1015776915614

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M,g) be a smooth compact Riemannian manifold, and G a subgroup of the isometry group of (M,g). We compute the value of the best constant in Sobolev inequalities when the functions are G-invariant. Applications to non-linear PDEs of critical or upper critical Sobolev exponent are also presented.

引用

页码：105 / 124

页数：20

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