Microlocal smoothing effect for the Schr\"odinger evolution equation in a Gevrey class

TL;DR

This paper investigates the microlocal Gevrey smoothing effect for the Schrödinger equation with variable coefficients, utilizing propagation properties of the wave front set and microlocal exponential estimates.

Contribution

It introduces a new approach to analyze the microlocal Gevrey smoothing effect for Schrödinger equations with variable coefficients using wave front set propagation.

Findings

Established microlocal Gevrey smoothing effect for variable coefficient Schrödinger equations.

Applied microlocal exponential estimates to prove smoothing results.

Extended understanding of wave front set propagation in Gevrey classes.

Abstract

We discuss the microlocal Gevrey smoothing effect for the Schr\"odinger equation with variable coefficients via the propagation property of the wave front set of homogenous type. We apply the microlocal exponential estimates in a Gevrey case to prove our result.