Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type

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Two Numerical Methods for the elliptic Monge-Ampère equation (2010, methodology): “This is comparable to the solutions presented in [8].”
A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two (2013, background): “1) when, despite the smoothness of the data f and g, this problem has no classical solutions, as it is the case for example when Ω = (0, 1)(2), f = 1, and g = 0 [11,20,37].”
{C}^0$ penalty methods for the fully nonlinear Monge-Ampère equation (2011, methodology): “Dean and Glowinski [15] presented an augmented Lagrange multiplier method and a least squares method for the Monge-Ampère equation by treating the nonlinear equations as a constraint and using a variational principle to select a particular solution.”
Finite element approximations of the three dimensional Monge-Ampère equation (2012, methodology): “Extending the previous work in [11], the authors used a least-squares methodology to compute the solution of the nonlinear problem.”