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arXiv · 1708.01307

Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators

Antonio Bove·Gregorio Chinni
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Abstract

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying H\"ormander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its subelliptic index it still has the Gevrey minimal regularity. We also prove a statement concerning real analytic hypoellipticity for the same type of pseudodifferential perturbations, provided the operator satisfies to some extra conditions (see Theorem 1.2 below) that ensure the analytic hypoellipticity.

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Antonio Bove, Gregorio Chinni. 2017-08-03. Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators. https://arxiv.org/abs/1708.01307

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