 I. Bakelman, Convex analysis and nonlinear geometric elliptic equations. SpringerVerlag, Germany (1994).
 G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal. 4 (1991) 271–283. [MathSciNet]
 K. Böhmer, On finite element methods for fully nonlinear elliptic equations of second order. SIAM J. Numer. Anal. 46 (2008) 1212–1249. [CrossRef] [MathSciNet]
 L.A. Caffarelli and M. Milman, Eds., Monge Ampère equation: applications to geometry and optimization, Contemporary Mathematics 226. American Mathematical Society, Providence, USA (1999).
 L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear secondorder elliptic equations. I. MongeAmpère equation. Comm. Pure Appl. Math. 37 (1984) 369–402. [CrossRef] [MathSciNet]
 M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1–67. [CrossRef] [MathSciNet]
 E.J. Dean and R. Glowinski, An augmented Lagrangian approach to the numerical solution of the Dirichlet problem for the elliptic MongeAmpère equation in two dimensions. Electron. Trans. Numer. Anal. 22 (2006) 71–96. [MathSciNet]
 E.J. Dean and R. Glowinski, Numerical methods for fully nonlinear elliptic equations of the MongeAmpère type. Comput. Methods Appl. Mech. Engrg. 195 (2006) 1344–1386. [CrossRef] [MathSciNet]
 E.J. Dean and R. Glowinski, On the numerical solution of the elliptic MongeAmpère equation in dimension two: a leastsquares approach, in Partial differential equations, Comput. Methods Appl. Sci. 16, Springer, Dordrecht, The Netherlands (2008) 43–63.
 E.J. Dean, R. Glowinski and T.W. Pan, Operatorsplitting methods and applications to the direct numerical simulation of particulate flow and to the solution of the elliptic MongeAmpère equation, in Control and boundary analysis, Lect. Notes Pure Appl. Math. 240, Chapman & Hall/CRC, Boca Raton, USA (2005) 1–27.
 L.C. Evans, Partial differential equations and MongeKantorovich mass transfer, in Current developments in mathematics, 1997 (Cambridge, MA), Int. Press, Boston, USA (1999) 65–126.
 X. Feng and M. Neilan, Galerkin methods for the fully nonlinear MongeAmpère equation. http://arxiv.org/abs/0712.1240v1 (2007).
 X. Feng and M. Neilan, Mixed finite element methods for the fully nonlinear MongeAmpère equation based on the vanishing moment method. SIAM J. Numer. Anal. 47 (2009) 1226–1250. [CrossRef] [MathSciNet]
 X. Feng and M. Neilan, Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations. J. Sci. Comput. 38 (2009) 74–98. [CrossRef] [MathSciNet]
 R. Glowinski, Numerical methods for fully nonlinear elliptic equations, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures, R. Jeltsch and G. Wanner Eds. (2009) 155–192.
 R. Glowinski, E.J. Dean, G. Guidoboni, L.H. Juárez and T.W. Pan, Applications of operatorsplitting methods to the direct numerical simulation of particulate and freesurface flows and to the numerical solution of the twodimensional elliptic MongeAmpère equation. Japan J. Indust. Appl. Math. 25 (2008) 1–63. [CrossRef] [MathSciNet]
 C.E. Gutiérrez, The MongeAmpère equation, Progress in Nonlinear Differential Equations and their Applications 44. Birkhäuser Boston Inc., Boston, USA (2001).
 G. Loeper and F. Rapetti, Numerical solution of the MongeAmpère equation by a Newton's algorithm. C. R. Math. Acad. Sci. Paris 340 (2005) 319–324. [CrossRef] [MathSciNet]
 A.M. Oberman, Convergent difference schemes for degenerate elliptic and parabolic equations: HamiltonJacobi equations and free boundary problems. SIAM J. Numer. Anal. 44 (2006) 879–895. [CrossRef] [MathSciNet]
 A.M. Oberman, Computing the convex envelope using a nonlinear partial differential equation. Math. Models Methods Appl. Sci. 18 (2008) 759–780. [CrossRef] [MathSciNet]
 A.M. Oberman, Wide stencil finite difference schemes for the elliptic MongeAmpère equation and functions of the eigenvalues of the Hessian. Discrete Contin. Dyn. Syst. Ser. B 10 (2008) 221–238. [CrossRef] [MathSciNet]
 V.I. Oliker and L.D. Prussner, On the numerical solution of the equation (∂^{2}z/∂x^{2})(∂^{2}z/∂y^{2})  (∂^{2}z/∂x∂y)^{2} = f and its discretizations, I. Numer. Math. 54 (1988) 271–293. [CrossRef] [MathSciNet]
Free access
Issue 
ESAIM: M2AN
Volume 44, Number 4, JulyAugust 2010



Page(s)  737  758  
DOI  http://dx.doi.org/10.1051/m2an/2010017  
Published online  23 February 2010 