Germ hypoellipticity and loss of derivatives

Chinni, Gregorio

doi:10.1090/S0002-9939-2011-11252-8

Germ hypoellipticity and loss of derivatives
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by Gregorio Chinni PDF

Proc. Amer. Math. Soc. 140 (2012), 2417-2427 Request permission

Abstract:

We prove hypoellipticity in the sense of germs for the operator \[ \mathcal {P}= L_{q}\overline {L}_{q} + \overline {L}_{q}t^{2k}L_{q} +Q^{2}, \] where \[ L_{q}=D_{t}+it^{q-1}\sqrt {-\Delta _{x}}\quad \text {and}\quad Q = x_{1}D_{2}-x_{2}D_{1}, \] even though it fails to be hypoelliptic in the strong sense. The primary tool is an a priori estimate.

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