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arXiv · 1711.00161

Hypoellipticity without loss of derivatives for Fedii's type operators

Timur Akhunov·Lyudmila Korobenko·Cristian Rios
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Abstract

We prove that second order linear operators on $\mathbb{R}^{n+m}$ of the form $L(x,y,D_x,D_y) = L_1(x,D_x) + g(x) L_2(y,D_y)$, where $L_1$ and $L_2$ satisfy Morimoto's super-logarithmic estimates and $g$ is smooth, nonnegative, and vanishes only at the origin in $\mathbb{R}^n$ (but to any arbitrary order) are hypoelliptic without loss of derivarives. We also show examples in which our hypotheses are necessary for hypoellipticity.

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Timur Akhunov, Lyudmila Korobenko, Cristian Rios. 2017-11-01. Hypoellipticity without loss of derivatives for Fedii's type operators. https://arxiv.org/abs/1711.00161

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