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A note on the Monge-Ampère type equations with general source terms (1611.03222v2)
Published 10 Nov 2016 in math.AP
Abstract: 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.