Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 2

Loss of derivatives in the infinite type

Pages: 315 – 327

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n2.a7

Authors

Tran Vu Khanh (School of Mathematics and Applied Statistics, University of Wollongong, NSW, Australia)

Stefano Pinton (Dipartimento di Matematica, Università di Padova, Italy)

Giuseppe Zampieri (Dipartimento di Matematica, Università di Padova, Italy)

Abstract

We prove hypoellipticity with loss of $\epsilon$ derivatives for a system of complex vector fields whose Lie-span has a superlogarithmic estimate. In $\mathbb{C} \times R$, the model is $(\overline{L}, \overline{f}^k L)$ where $\overline{f} = \overline{z} h$ for $h \neq 0$ and $L$ is the vector field tangential to the exponentially non-degenerate hypersurface of infinite type defined by $x_2 = e^{- \frac{1}{\lvert z \rvert^\alpha}}$ for $\alpha \lt 1$.

Keywords

hypoellipticity, loss of derivatives, superlogarithmic estimate, infinite type

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