Analytic Hypoellipticity for a Class of Sums of Squares of Vector Fields with Non-Symplectic Characteristic Variety

Details Analytic Hypoellipticity for a Class of Sums of Squares of Vector Fields with Non-Symplectic Characteristic Variety Analytic Hypoellipticity for a Class of Sums of Squares of Vector Fields with Non-Symplectic Characteristic Variety

2005-04-07

arxiv.org/abs/math/0504159v1

Journal of Functional Analysis {\bf 234} (2), (2006), pp~464-472.

Mathematics

Analysis of PDEs

11 pages

Scientific paper

The recent example of Hanges: $P = \partial_t^2 + t^2\Delta_x + \partial^2_{\theta(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs but not in the strong sense in any neighborhood of the origin. And its characteristic variety is non-symplectic. We give a purely $L^2,$ and hence quite flexible, proof of this result and generalizations, and link it to, and contrast it with, the celebrated Baouendi-Goulaouic operator. We point out that the results are consistent with the conjecture of Treves.

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