We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying Hörmander’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.

Bove, A., Chinni, G. (2018). Analytic and Gevrey hypoellipticity for perturbed sums of squares operators. ANNALI DI MATEMATICA PURA ED APPLICATA, 197(4), 1201-1214 [10.1007/s10231-017-0720-x].

Analytic and Gevrey hypoellipticity for perturbed sums of squares operators

Bove, Antonio;Chinni, Gregorio
2018

Abstract

We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying Hörmander’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.
2018
Bove, A., Chinni, G. (2018). Analytic and Gevrey hypoellipticity for perturbed sums of squares operators. ANNALI DI MATEMATICA PURA ED APPLICATA, 197(4), 1201-1214 [10.1007/s10231-017-0720-x].
Bove, Antonio*; Chinni, Gregorio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/678322
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