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

Qiu, Weifeng; Tang, Lan

doi:10.1090/mcom/3554

A note on the Monge–Ampère type equations with general source terms
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Math. Comp. 89 (2020), 2675-2706 Request permission

Abstract:

In this paper we consider numerical approximation to the generalised solutions to the Monge–Ampère type equations with general source terms. We first give some important propositions for the border of generalised solutions. Then, for both the classical and weak Dirichlet boundary conditions, we present well-posed numerical methods for the generalised solutions with general source terms. Finally, we prove that the numerical solutions converge to the generalised solution.

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