Chapter

Advances in Phase Space Analysis of Partial Differential Equations

Volume 78 of the series Progress in Nonlinear Differential Equations and Their Applications pp 253-261

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Analytic Hypoellipticity for a Sum of Squares of Vector Fields in ℝ3 Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four

  • David S. TartakoffAffiliated withDepartment of Mathematics, University of Illinois at Chicago Email author 

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Summary

We prove analytic hypoellipticity for a sum of squares of vector fields in ℝ3 all of whose Poisson strata are equal and symplectic of codimension four, extending in a model setting the recent general result of Cordaro and Hanges in codimension two [2]. The easy model we study first and then its easy generalizations possess a divisibility property reminiscent of earlier work of the author and Derridj in [3] and Grigis–Sjöstrand in [4].

Keywords

Analytic Sum of squares Poisson stratification