Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields
Copyright policy )Hypoellipticity and nonhypoellipticity for sums of squares of complex vector fields
In this talk we consider the analogue of Kohn’s operator but with a point singularity, P = BB∗ +B∗(t2` + x)B, B = Dx + ix Dt. We show that this operator is hypoelliptic and Gevrey hypoelliptic in a certain range, namely k < `q, with Gevrey index `q `q−k = 1 + k `q−k . Outside the above range of the parameters, i.e. when k ≥ `q, the operator is not even hypoelliptic.
- University of Illinois at Chicago United States
- Alma Mater Studiorum University of Bologna Italy
35B65, sums of squares of complex vector fields; hypoellipticity; Gevrey hypoellipticity; pseudodifferential operators, Gevrey hypoellipticity, hypoellipticity, 35H10, pseudodifferential operators, 35H20, sums of squares of complex vector fields
35B65, sums of squares of complex vector fields; hypoellipticity; Gevrey hypoellipticity; pseudodifferential operators, Gevrey hypoellipticity, hypoellipticity, 35H10, pseudodifferential operators, 35H20, sums of squares of complex vector fields
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