Global Gevrey hypoellipticity for the twisted Laplacian on forms

TL;DR

This paper investigates the global Gevrey hypoellipticity of the generalized twisted Laplacian acting on differential forms, revealing anisotropic regularity properties despite the operator's local ellipticity and global degeneracy.

Contribution

It extends the analysis of hypoellipticity to systems on forms, demonstrating global Gevrey regularity for a class of degenerate elliptic operators.

Findings

Established global Gevrey hypoellipticity for the twisted Laplacian on forms.

Identified anisotropic regularity properties in the Gevrey category.

Analyzed the operator's behavior beyond the scalar case, accounting for degeneracy.

Abstract

We study in this paper the global hypoellipticity property in the Gevrey category for the generalized twisted Laplacian on forms. Different from the 0-form case, where the twisted Laplacian is a scalar operator, this is a system of differential operators when acting on forms, each component operator being elliptic locally and degenerate globally. We obtain here the global hypoellipticity in anisotropic Gevrey space.