A NOTE ON EXTREMAL FUNCTIONS FOR SHARP SOBOLEV INEQUALITIES

被引：0
|
作者：
Barbosa, Ezequiel R. [1 ]
Montenegro, Marcos [1 ]
机构：
[1] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG, Brazil
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年
关键词：
Extremal functions; optimal Sobolev inequalities; conformal deformations;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we prove that any compact Riemannian manifold of dimension n >= 4 which is non-conformal to the standard n-sphere and has positive Yamabe invariant admits infinitely many conformal metrics with nonconstant positive scalar curvature on which the classical sharp Sobolev inequalities admit extremal functions. In particular we show the existence of compact Riemannian manifolds with nonconstant positive scalar curvature for which extremal functions exist. Our proof is simple and bases on results of the best constants theory and Yamabe problem.
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页数：5
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