On $L^p$ resolvent estimates for elliptic operators on compact manifolds

Katsiaryna Krupchyk; Gunther Uhlmann

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arXiv · 1304.0048

On $L^p$ resolvent estimates for elliptic operators on compact manifolds

Katsiaryna Krupchyk·Gunther Uhlmann

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Abstract

We prove uniform $L^p$ 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 $L^p$ resolvent estimates are optimal.

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Katsiaryna Krupchyk, Gunther Uhlmann. 2013-03-30. On $L^p$ resolvent estimates for elliptic operators on compact manifolds. https://arxiv.org/abs/1304.0048

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