On L p Resolvent Estimates for Elliptic Operators on Compact Manifolds

被引：6

作者：

Krupchyk, Katsiaryna ^{[1
]}

Uhlmann, Gunther ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 40卷 / 03期

基金：

芬兰科学院; 美国国家科学基金会;

关键词：

Uniform estimate; Resolvent; Elliptic operator; Functional calculus; CLUSTERS;

D O I：

10.1080/03605302.2014.966391

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove uniform L ( p ) estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding result of [3] in the case of Laplace-Beltrami operators on Riemannian manifolds. In doing so, we follow the methods, developed in [1] very closely. We also show that spectral regions in our L ( p ) resolvent estimates are optimal.

引用

页码：438 / 474

页数：37

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