The Semiclassical Resolvent on Conic Manifolds and Application to Schr\"odinger Equations
Analysis of PDEs
2021-06-02 v2
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 Schr\"odinger equations on non-compact manifolds with multiple non-product conic singularities.
Keywords
Cite
@article{arxiv.2009.12895,
title = {The Semiclassical Resolvent on Conic Manifolds and Application to Schr\"odinger Equations},
author = {Xi Chen},
journal= {arXiv preprint arXiv:2009.12895},
year = {2021}
}