A note on the Monge-Ampère type equations with general source terms

Abstract

In this paper we consider the generalised solutions to the Monge-Amp{è}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.