Alvarez O., Lasry J.-M., Lions P.-L.: Convex viscosity solutions and state constraints. J. Math. Pures Appl. 76(3), 265–288 (1997)
Abbasi, B., Oberman, A.M.: A partial differential equation for the strictly quasiconvex envelope. arXiv:1612.06813, 2016
Aranda E., Pedregal P.: Numerical approximation of non-homogeneous, non-convex vector variational problems. Numer. Math. 89(3), 425–444 (2001)
Aranda E., Pedregal P.: On the computation of the rank-one convex hull of a function. SIAM J. Sci. Comput. 22(5), 1772–1790 (2001)
Ball, J.M.: Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal. 63(4), 337–403, 1976/1977
Bartels S.: Linear convergence in the approximation of rank-one convex envelopes. ESAIM: Math. Model. Numer. Anal. 38(05), 811–820 (2004)
Bartels S.: Reliable and efficient approximation of polyconvex envelopes. SIAM J. Numer. Anal. 43(1), 363–385 (2005)
Ball, J., James, R.: Fine phase mixtures as minimizers of energy. In: Analysis and Continuum Mechanics, pp. 647–686. Springer, Berlin, 1989
Ball J.M., Kirchheim B., Kristensen J.: Regularity of quasiconvex envelopes. Calc. Var. Partial Differ. Equ. 11(4), 333–359 (2000)
Bardi M., Mannucci P.: On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Commun. Pure Appl. Anal. 5(4), 709–731 (2006)
Bardi, M., Mannucci, P.: Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge–Ampère type. In: Forum Mathematicum, vol. 25, pp. 1291–1330, 2013
Barles G., Souganidis P.E.: Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4(3), 271–283 (1991)
Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27(1), 1–67, 1992
Chipot M., Kinderlehrer D.: Equilibrium configurations of crystals. Arch. Ration. Mech. Anal. 103(3), 237–277 (1988)
Caffarelli L.A., Nirenberg L., Spruck J.: The dirichlet problem for the degenerate monge-ampère equation. Rev. Mat. Iberoam. 2(1–2), 19–27 (1986)
Dacorogna, B.: Direct Methods in the Calculus of Variations. Applied Mathematical Sciences, 2nd edn, vol. 78. Springer, Berlin, 2008
Dolzmann, G.: Numerical computation of rank-one convex envelopes. SIAM J. Numer. Anal. 36(5), 1621–1635, 1999 (electronic)
Dolzmann, G.: Variational Methods for Crystalline Microstructure-Analysis and Computation. Number 1803. Springer, 2003
De Philippis, G., Figalli, A.: Optimal regularity of the convex envelope. Trans. Am. Math. Soc. 367(6), 4407–4422, 2015
Dolzmann G., Walkington N.J.: Estimates for numerical approximations of rank one convex envelopes. Numer. Math. 85(4), 647–663 (2000)
Franěk V., Matoušek J.: Computing d-convex hulls in the plane. Comput. Geom. 42(1), 81–89 (2009)
Froese B.D., Oberman A.M.: Convergent filtered schemes for the Monge–Ampère partial differential equation. SIAM J. Numer. Anal. 51(1), 423–444 (2013)
Froese, B.D.: Convergent approximation of surfaces of prescribed Gaussian curvature with weak Dirichlet conditions. arXiv:1601.06315, 2016
Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn, vol. 224. Springer, Berlin, 1983
Kohn R.V., Strang G.: Optimal design and relaxation of variational problems, i. Commun. Pure Appl. Math. 39(1), 113–137 (1986)
Kohn R.V., Strang G.: Optimal design and relaxation of variational problems, ii. Commun. Pure Appl. Math. 39(2), 139–182 (1986)
Morrey C.B.: Quasi-convexity and the lower semicontinuity of multiple integrals. Pac. J. Math. 2(1), 25–53 (1952)
Matoušek J., Plecháč P.: On functional separately convex hulls. Discrete Comput. Geom. 19(1), 105–130 (1998)
Muller, S.: Variational models for microstructure and phase transitions. In: Calculus of Variations and Geometric Evolution Problems (Italy, 1996), pp. 85–210. Springer, Berlin, 1999
Motzkin T.S., Wasow W.: On the approximation of linear elliptic differential equations by difference equations with positive coefficients. J. Math. Phys. 31, 253–259 (1953)
Oberman, A.M.: Convergent difference schemes for degenerate elliptic and parabolic equations: Hamilton–Jacobi equations and free boundary problems. SIAM J. Numer. Anal. 44(2), 879–895, 2006 (electronic)
Oberman, A.M.: The convex envelope is the solution of a nonlinear obstacle problem. Proc. Am. Math. Soc. 135(6), 1689–1694, 2007 (electronic)
Oberman A.M.: Computing the convex envelope using a nonlinear partial differential equation. Math. Models Methods Appl. Sci. 18(5), 759–780 (2008)
Oberman A.M.: Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete Contin. Dyn. Syst. Ser. B, 10(1), 221–238 (2008)
Oberman A., Silvestre L.: The Dirichlet problem for the convex envelope. Trans. Am. Math. Soc. 363(11), 5871–5886 (2011)
Pedregal, P.: Parametrized Measures and Variational Principles, vol. 30. Springer, 1997