Global analytic, Gevrey and C∞ hypoellipticity on the 3-torus
✍ Scribed by A. Alexandrou Himonas; Gerson Petronilho; L. A. Carvalho dos Santos
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 223 KB
- Volume
- 285
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
It is proved that a class of sub‐Laplacians on the 3‐dimensional torus is globally analytic, Gevrey and C^∞^ hypoelliptic if and only if either a Diophantine condition holds or there is a point of finite type for the vector fields defining the operator under consideration. This work is motivated by the desire of attaining a better understanding of necessary and sufficient conditions for the global Gevrey and C^∞^ hypoellipticity of a sub‐Laplacian on a compact analytic manifold. This together with the more delicate local hypoellipticity are well‐known open problems in the theory of linear partial differential equations.