arXiv:2009.12895 Abstract | arXiv Analytics

arXiv:2009.12895 [math.AP]Abstract References Reviews Resources

The Semiclassical Resolvent on Conic Manifolds and Application to Schrödinger Equations

Published 2020-09-27Version 1

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.

Categories: math.AP

Keywords: schrödinger equations, semiclassical resolvent, application, multiple non-product conic singularities, non-product conic manifolds

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