CRIS Current Research Information System
IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili.
EnglishWe 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.
| Titolo: | On a new method of proving Gevrey hypoellipticity for certain sums of squares | |
| Autore/i: | BOVE, ANTONIO; MUGHETTI, MARCO | |
| Autore/i Unibo: | ||
| Anno: | 2016 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aim.2016.02.009 | |
| 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. | |
| Data stato definitivo: | 2021-03-19T12:25:00Z | |
| Appare nelle tipologie: |
File in questo prodotto:
Copyright © 2022