Smoothness of the fundamental solution of Schrödinger equations with mild trapping

2022/03/03 by Taira, Kouichi
#35A08 #35A21 #35R01 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.01499

Abstract

In this short note, smoothness of the fundamental solution of Schrödinger equations on a complete manifold is studied. It is shown that (1) the fundamental solution is smooth under "mild" trapping conditions; (2) there is a Riemannian manifold which is equal to Euclidean space outside a compact set such that the fundamental solution is not smooth.

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