We consider an operator being a sum of squares of vector fields. It has the form, p,r∈N, P(x,Dx,Dy,Dt)=Dx2+x2(p-1)(Dy-xrDt)2. This type of operator is C∞ hypoelliptic by Hörmander's theorem, [18]. Its analytic or Gevrey hypoellipticity has then been studied by a number of authors and is relevant in relation to the Treves conjecture. The Poisson-Treves stratification of P includes both symplectic and non-symplectic strata.In this paper we show that P is Gevrey (p+. r)/. p hypoelliptic, by constructing a parametrix whose symbol belongs to some exotic classes. One can also show that this number is optimal.
Bove, A., Mughetti, M. (2016). On a new method of proving Gevrey hypoellipticity for certain sums of squares. ADVANCES IN MATHEMATICS, 293, 146-220 [10.1016/j.aim.2016.02.009].
On a new method of proving Gevrey hypoellipticity for certain sums of squares
BOVE, ANTONIO;MUGHETTI, MARCO
2016
Abstract
We consider an operator being a sum of squares of vector fields. It has the form, p,r∈N, P(x,Dx,Dy,Dt)=Dx2+x2(p-1)(Dy-xrDt)2. This type of operator is C∞ hypoelliptic by Hörmander's theorem, [18]. Its analytic or Gevrey hypoellipticity has then been studied by a number of authors and is relevant in relation to the Treves conjecture. The Poisson-Treves stratification of P includes both symplectic and non-symplectic strata.In this paper we show that P is Gevrey (p+. r)/. p hypoelliptic, by constructing a parametrix whose symbol belongs to some exotic classes. One can also show that this number is optimal.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
