Criteria for hypoellipticity of differential operators
The author studies \(L^ 2\) estimates which imply hypoellipticity of partial differential operators. As a consequence he proves e.g. the hypoellipticity of the operators \[ D_ 1^{2\ell}+D_ 2^{2\ell}+\exp (-| x_ 1|^{-\delta})D_ 3^{2\ell}\quad in\quad {\mathbb{R}}^ 3,\quad \ell \in {\mathbb{Z}}^+/\{0\},\quad 0<\delta <1, \] and \(D_ 1^{2\ell}+\exp (-| x_ 1|^{-\delta})D_ 2^{2\ell}\) in \({\mathbb{R}}^ 2\), \(\ell \in {\mathbb{Z}}^+\setminus \{0\}\), \(\delta >0\).
scientific article; zbMATH DE number 4063617