English

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 LpL^p 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 LpL^p 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}
}