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On the regularity of the Monge-Ampère equation $$\text{det}(\partial^2u/\partial x_1\partial x_j)=F(x,u)$$. (English) Zbl 0347.35019

MSC:
 35D10 Regularity of generalized solutions of PDE (MSC2000) 53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov) 35D05 Existence of generalized solutions of PDE (MSC2000) 35G20 Nonlinear higher-order PDEs
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References:
 [1] Alexandrov, Vestnik Leningrad Univ. Ser. Mat. Mekh. Astr. 13 pp 5– (1958) [2] Calabi, Mich. Math. J. 5 pp 105– (1958) [3] Calabi, Ist. Naz. Alta Mat., Symp. Math. pp 19– (1972) [4] Cheng, Comm. Pure Appl. Math. [5] Monge-Ampère Equations of Elliptic Type, Noordhoff, Groningen, 1964. [6] Pogorelov, Dokl. Akad. Nauk SSSR 199 pp 1971– [7] Soviet Math. Dokl. 12 pp 1192– (1971) [8] Pogorelov, Dokl. Akad. Nauk SSSR 200 pp 534– (1971) [9] Soviet Math. Dokl. 12 pp 1436– (1971) [10] Pogorelov, Dokl. Akad. Nauk SSSR 201 pp 790– (1971) [11] Soviet Math. Dokl. 12 pp 1727– (1971)
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