In this paper we consider the generalised solutions to the Monge-Amp{\`{e}}re type equations with general source terms. We firstly prove the so-called comparison principle and then give some important propositions for the border of generalised solutions. Furthermore, we design well-posed finite element methods for the generalised solutions with the classical and weak Dirichlet boundary conditions respectively.

中文翻译：

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关于具有一般源项的 Monge-Ampère 类型方程的注释

在本文中，我们考虑了具有一般源项的 Monge-Amp{\`{e}}re 类型方程的广义解。我们首先证明了所谓的比较原理，然后给出了广义解的边界的一些重要命题。此外，我们分别为经典和弱狄利克雷边界条件的广义解设计了适定的有限元方法。