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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Bove et al. (2026) studied this question.
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