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.
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页码：438 / 474
页数：37
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