We study the Gevrey hypoellipticity of a sum of two squares in two variables, satisfying the H\"ormander 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.
Bove, A., Mughetti, M. (2026). Gevrey regularity for a sum of two squares in two variables. PURE AND APPLIED FUNCTIONAL ANALYSIS, 11(3), 529-547.
Gevrey regularity for a sum of two squares in two variables
Bove A.;Mughetti M.
2026
Abstract
We study the Gevrey hypoellipticity of a sum of two squares in two variables, satisfying the H\"ormander 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.File in questo prodotto:
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