Finite element approximations of the three dimensional Monge-Ampère equation

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{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation (2011, methodology): “• The method and analysis can be extended to the three-dimensional setting [8].”
A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two (2013, methodology): “Perspectives include the extension of this methodology to other fully nonlinear elliptic equations in two and three dimensions of space in arbitrary domains [7, 26].”