On $L^p$ resolvent estimates for elliptic operators on compact manifolds
Analysis of PDEs
2013-04-02 v1 Classical Analysis and ODEs
Abstract
We prove uniform estimates for resolvents of higher order elliptic self-adjoint differential operators on compact manifolds without boundary, generalizing a corresponding resul 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 resolvent estimates are optimal.
Keywords
Cite
@article{arxiv.1304.0048,
title = {On $L^p$ resolvent estimates for elliptic operators on compact manifolds},
author = {Katsiaryna Krupchyk and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1304.0048},
year = {2013}
}