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On the regularity of the solution of the \(n\)-dimensional Minkowski problem. (English) Zbl 0363.53030


MSC:

53C65 Integral geometry
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
35G20 Nonlinear higher-order PDEs
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References:

[1] and , Theorie der Konvexen Körper, Chelsa, N.Y., 1948.
[2] Convex Surfaces Wiley-Intersceience, New York, 1948.
[3] Calabi, Mich. Math. J. 5 pp 105– (1958)
[4] and , On the rgularity of the Monge–Ampère equation det (2 u/xj xj) = F(x, u), to appear in Comm. Pure Appl. Math., 1977.
[5] Convexity Cambridge Univ. Press, Cambridge, 1948.
[6] Nirenberg, Comm. Pure Appl. Math. 6 pp 337– (1953)
[7] Pogorelov, Soviet Math. Dokl. 12 pp 1436– (1971)
[8] Pogorelov, Soviet Math. Dokl. 12 pp 1192– (1971)
[9] Pogorelov, Russian, Mat. Sbornik N. S. 31 pp 88– (1952)
[10] Nonlinear Functional Analysis, Gordon and Breach, N. Y., 1968.
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