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arXiv · 1507.02307

From semiclassical Strichartz estimates to uniform $L^p$ resolvent estimates on compact manifolds

Nicolas Burq·David Dos Santos Ferreira·Katya Krupchyk
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Abstract

We prove uniform $L^p$ resolvent estimates for the stationary damped wave operator. The uniform $L^p$ resolvent estimates for the Laplace operator on a compact smooth Riemannian manifold without boundary were first established by Dos Santos Ferreira-Kenig-Salo and advanced further by Bourgain-Shao-Sogge-Yao. Here we provide an alternative proof relying on the techniques of semiclassical Strichartz estimates. This approach allows us also to handle non-self-adjoint perturbations of the Laplacian and embeds very naturally in the semiclassical spectral analysis framework.

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Nicolas Burq, David Dos Santos Ferreira, Katya Krupchyk. 2015-07-08. From semiclassical Strichartz estimates to uniform $L^p$ resolvent estimates on compact manifolds. https://arxiv.org/abs/1507.02307

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