Loss of derivatives in the infinite type

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

Full Text (PDF format)

Published 24 August 2016