References
Bakelman, I.J.: Variational problem connected with Monge-Ampère equations. Dokl. Akad. Nauk. USSR141, 1011–1014 (1961)
Bakelman, I.J.: Variational problems and elliptic Monge-Ampère equations. J. Differ. Geom.18, 669–699 (1983)
Caffarelli, L., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear secon order elliptic equations. Commun. Pure Appl. Math.37, 369–402 (1984)
Cheng, S.Y., Yau, S.T.: On the regularity of the Monge-Ampère equation det (∂2 u/∂x i ∂x j ) =F(x, u). Commun. Pure Appl. Math.37, 41–68 (1977)
Evan, L.C.: Classical solutions of fully nonlinear, convex, second order elliptic equations. Commun. Pure Appl. Math.35, 333–363 (1982)
Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs: Prentice-Hall. 1964
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. 2nd edn. Berlin, Heidelberg, New York: Springer 1983
Krylov, N.V.: Bounded inhomogeneous elliptic and parabolic equations. Math. USSR, Izv.20, 459–492 (1983)
Krylov, N.V.: Estimates for derivatives of the solution of nonlinear parabolic equations. Dokl. Akad. USSR274, 23 (1984)
Ladyzenskaja, O.A., Solonnikov, V.A., Uralceva, N.N.: Linearand quasilinear equations of parabolic type. Trans. Am. Math. Soc. Vol. 23, 1968
Lions, P.L.: Sur les equations de Monge-Ampère. Arch. Ration. Mech. Anal.89, 93–122 (1985)
Lions, P.L.: Two remarks on Monge-Ampère equations. Ann. Mat. Puro. Appl.142, 263–275 (1985)
Pogorelov, A.V.: The multidimensional Minkowski problem. New York: Wiley 1978
Rabinowitz, P.H.: Minimax methods in critical point theory with applications to differential equations. Expository Lectures from the CBMS Regional Conference. Am. Math. Soc. Vol.65, 1986
Tso, K.: Remarks on the critical exponents for the Hessian operators. Ann. Inst. H. Poincaré Anal. Nonlinéaire (to appear)
Urbas, J.I.E.: Elliptic equations of Monge-Ampère type. Thesis, The Australian National University. 1984
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Oblatum 17-VII-1989
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Tso, K. On a real Monge—Ampère functional. Invent Math 101, 425–448 (1990). https://doi.org/10.1007/BF01231510
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DOI: https://doi.org/10.1007/BF01231510