Gevrey Regularity for a Sum of Two Squares in Two Variables

We study the Gevrey hypoellipticity of a sum of two squares in two variables, satisfying the Hörmander hypothesis, assuming that the function, $ q $, describing (the space projection of) its characteristic variety vanishes only at a single point, which can be assumed to be the origin. A hypoellipticity result is given in a Gevrey class, depending on $ q $. In some examples the found regularity is known to be optimal.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.35427
Primary Topic
Mathematical and Theoretical Analysis
Type
preprint
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preprint

Gevrey Regularity for a Sum of Two Squares in Two Variables

Marco Mughetti, Antonio Bove
arXiv (Cornell University)
Mathematical and Theoretical Analysis
preprint

Gevrey Regularity for a Sum of Two Squares in Two Variables

Marco Mughetti, Antonio Bove
preprint en

Abstract

We study the Gevrey hypoellipticity of a sum of two squares in two variables, satisfying the Hörmander hypothesis, assuming that the function, $ q $, describing (the space projection of) its characteristic variety vanishes only at a single point, which can be assumed to be the origin. A hypoellipticity result is given in a Gevrey class, depending on $ q $. In some examples the found regularity is known to be optimal.

arXiv (Cornell University)
Mathematical and Theoretical Analysis
DOIOpen Access PDFOpenAlex
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Gevrey Regularity for a Sum of Two Squares in Two Variables — Marco Mughetti, Antonio Bove · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS