DENSITY PROBLEMS ON VECTOR BUNDLES AND MANIFOLDS

被引：11

作者：

Bandara, Lashi ^{[1
]}

机构：

[1] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 142卷 / 08期

关键词：

Density problems; first order operators on vector bundles; Laplacian on vector bundles; second order Sobolev spaces on manifolds; SQUARE-ROOT PROBLEM;

D O I：

10.1090/S0002-9939-2014-12284-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.

引用

页码：2683 / 2695

页数：13

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