Dispersive estimates for the Schrodinger equation in dimensions four and five

TL;DR

This paper establishes optimal dispersive estimates for the Schrödinger equation in four and five dimensions with certain regular potentials, improving understanding of wave behavior in these settings.

Contribution

It provides the first proof of optimal dispersive estimates without loss of derivatives for dimensions four and five with specified potential regularity.

Findings

Optimal dispersive estimates proven for n=4,5

No loss of derivatives in the estimates

Applicable to potentials with regularity k>(n-3)/2

Abstract

We prove optimal (that is, without loss of derivatives) dispersive estimates for the Schrodinger group $e^{it(-\Delta+V)}$ for a class of real-valued potentials $V\in C^k(R^n)$ with $k>(n-3)/2$, where $n=4,5$.