This paper studies some systems of second order partial differential equations associated to a Dirac type operator \({^\varphi \!\underline{\partial }}\) in \({\mathbb {R}}^2\) and \({\mathbb {R}}^3\), with respect to an arbitrary structural set \(\varphi \). We develop a method by which we can transform these general systems into those connected to the standard Dirac operator \(\underline{\partial }\). One unexpected result is that there exists an isomorphism relating the above generalized equations to the original ones.

中文翻译：

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Clifford分析中偏微分方程的同构

本文研究了与狄拉克类型算子\({^\varphi \!\underline{\partial }}\)在\({\mathbb {R}}^2\)和\ ({\mathbb {R}}^3\)，关于任意结构集\(\varphi \)。我们开发了一种方法，通过该方法我们可以将这些通用系统转换为与标准狄拉克算子\(\underline{\partial }\)相连的系统。一个意想不到的结果是存在将上述广义方程与原始方程相关联的同构。