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A class of hypoelliptic PDE admitting non-analytic solutions. (English) Zbl 0804.35022
Complex analysis, Proc. Symp., Madison/WI (USA) 1992, Contemp. Math. 137, 155-167 (1992).
[For the entire collection see Zbl 0755.00016.]
The author deals with a special class of partial differential operators having the form of sums of squares of two vector fields in \(\mathbb{R}^ 3\). The coefficients are supposed to be real-analytic. It is well known that this class is \(C^ \infty\) hypoelliptic. The author proves here that the operators under consideration are not analytic hypoelliptic. To do this a very precise asymptotic analysis of a two-parameter family of ordinary differential equations is proposed. This paper is a continuation of some previous investigations of Christ as well as of some investigations of Hanges-Himonas.

35G05 Linear higher-order PDEs
65H10 Numerical computation of solutions to systems of equations