8 papers
On a class of globally analytic Hypoelliptic operators with non-negative characteristic form
Nicholas Braun Rodrigues, Gregorio Chinni
The global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The cl…
On the Microlocal Regularity of the Gevrey Vectors for second order partial differential operators with non negative characteristic form of first kind
Gregorio Chinni, Makhlouf Derridj
We study the microlocal regularity of the analytic/Gevrey vectors for the following class of second order partial differential equations \begin{align*} P(x,D) = \sum_{\ell,j=1}^{n}…
On the microlocal regularity of the analytic vectors for "sums of squares" of vector fields
Gregorio Chinni, Makhlouf Derridj
We prove via FBI-transform a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic co…
(Semi-)Global Analytic Hypoellipticity for a class of "sums of squares" which fail to be locally analytic hypoelliptic
Gregorio Chinni
The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in "Analytic Hypoellipticity for Sums of Squares…
On a Class of Globally Analytic Hypoelliptic Sums of Squares
Antonio Bove, Gregorio Chinni
We consider sums of squares operators globally defined on the torus. We show that if some assumptions are satisfied the operators are globally analytic hypoelliptic. The purpose of…
On the sharp Gevrey regularity for a generalization of the Métivier operator
Gregorio Chinni
The sharp Gevrey hypoellipticity is provided for the following generalization of the Métivier operator, "Non-hypoellipticité analytique pour $D_{x}^{2}+\left( x^{2} + y^{2}\right)D…
Analytic and Gevrey Hypoellipticity for Perturbed Sums of Squares Operators
Antonio Bove, Gregorio Chinni
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…
On the Gevrey regularity for Sums of Squares of vector fields, study of some models
Gregorio Chinni
The micro-local Gevrey regularity of a class of "sums of squares" with real analytic coefficients is studied in detail. Some partial regularity result is also given.