Abstract
In this paper we consider a model sum of squares of complex vector fields in the plane, close to Kohn’s operator but with a point singularity,
The characteristic variety of is the symplectic real analytic manifold . We show that this operator is -hypoelliptic and Gevrey hypoelliptic in , the Gevrey space of index , provided , for every . We show that in the Gevrey spaces below this index, the operator is not hypoelliptic. Moreover, if , the operator is not even hypoelliptic in . This fact leads to a general negative statement on the hypoellipticity properties of sums of squares of complex vector fields, even when the complex Hörmander condition is satisfied.
Citation
Antonio Bove. Marco Mughetti. David Tartakoff. "Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields." Anal. PDE 6 (2) 371 - 445, 2013. https://doi.org/10.2140/apde.2013.6.371
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