Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665194 | Advances in Mathematics | 2016 | 75 Pages |
Abstract
We consider an operator being a sum of squares of vector fields. It has the form, p,r∈Np,r∈N,P(x,Dx,Dy,Dt)=Dx2+x2(p−1)(Dy−xrDt)2. This type of operator is C∞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(p+r)/p hypoelliptic, by constructing a parametrix whose symbol belongs to some exotic classes. One can also show that this number is optimal.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Antonio Bove, Marco Mughetti,