Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields

Details Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields

2006-09-28

arxiv.org/abs/math/0609777v1

Mathematics

Analysis of PDEs

20pp

Scientific paper

We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \sigma $ is not constant on $ \Char P $. Moreover the Hamilton foliation of the non symplectic stratum of the Poisson-Treves stratification for $ P $ consists of closed curves in a ring-shaped open set around the origin. We prove that then $ P $ is analytic hypoelliptic on that open set. And we note explicitly that the local Gevrey hypoellipticity for $ P $ is $ G^{k+1} $ and that this is sharp.

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