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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:
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[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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