The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations

2020/09/27 by Chen, Xi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.12895

Abstract

In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators, scattering pseudodifferential operators and intersecting Legendrian distributions. As an application, we shall establish Strichartz estimates for Schrödinger equations on non-compact manifolds with multiple non-product conic singularities.

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