Sobolev type inequalities on Riemannian manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:371

Article

Adriano, Levi²  Xia, Changyu¹ 

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Univ Fed Goias, Inst Matemat & Estat, BR-74001900 Goiania, Go, Brazil

关键词: Gagliardo-Nirenberg inequalities;    Log-Sobolev inequalities;    Riemannian manifolds;    Asymptotically non-negative Ricci curvature;    Maximal volume growth;   

DOI  :  10.1016/j.jmaa.2010.05.043

来源: Elsevier

【 摘 要 】

This paper studies Sobolev type inequalities on Riemannian manifolds. We show that on a complete non-compact Riemannian manifold the constant in the Gagliardo-Nirenberg inequality cannot be smaller than the optimal one on the Euclidean space of the same dimension. We also show that a complete non-compact manifold with asymptotically non-negative Ricci curvature admitting some Gagliardo-Nirenberg inequality is not very far from the Euclidean space. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free