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Gevrey Regularity for a Sum of Two Squares in Two Variables
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.
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BibTeX
@misc{bove2026gevrey,
title = {{Gevrey Regularity for a Sum of Two Squares in Two Variables}},
author = {Antonio Bove and Marco Mughetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35427},
eprint = {2610.35427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35427},
}
RIS
TY - UNPB
TI - Gevrey Regularity for a Sum of Two Squares in Two Variables
AU - Antonio Bove
AU - Marco Mughetti
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35427
UR - https://arxiv.org/abs/2610.35427
AB - 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.
ER -