The presence of symplectic strata improves the Gevrey regularity for sums of squares
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We consider a class of operators of the type sum of squares of real analytic vector fields satisfying the Hörmander bracket condition. The Poisson-Treves stratification is associated to the vector fields. We show that if the deepest stratum in the stratification, i.e., the stratum associated to the longest commutators, is symplectic, then the Gevrey regularity of the solution is better than the minimal Gevrey regularity given by the Derridj-Zuily theorem.
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- P. Albano and A. Bove, Wave front set of solutions to sums of squares of vector fields, Mem. Amer. Math. Soc. 221 (2013), no. 1039.Google Scholar
- P. Albano, A. Bove, and G. Chinni, Minimal microlocal Gevrey regularity for “sums of squares”, Int. Math. Res. Not. IMRN, 2009, 2275–2302.Google Scholar
- J. Sjöstrand, Singularités analytiques microlocales, Astérisque 95 (1982).Google Scholar