About Pogorelov's Method and Aleksandrov's Estimates
DOI:
https://doi.org/10.15407/mag16.03.283Анотація
Ми даємо короткий огляд ролі оцінок Александрова та ідей Погорєлова у наших дослідженнях.Mathematics Subject Classification: 35-01, 35-03, 51-01
Ключові слова:
оцінка Александрова, метод Погорєлова, рівняння БеллманаПосилання
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I.Ja. Bakelman, Geometric Methods of Solution of Elliptic Equations, Nauka, Moscow, 1965 (Russian).
Shiu Yuen Cheng and Shing Tung Yau, On the regularity of the Monge–Ampère equation det(∂ 2 u/∂xi ∂xj ) = F (x, u), Comm. Pure Appl. Math. 30 (1977), No. 1, 41–68.
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N.V. Krylov, Weighted Aleksandrov estimates: PDE and stochastic versions, Algebra i Analiz 31 (2019), No. 3, 154–169. https://doi.org/10.1090/spmj/1611
A.V. Pogorelov, The regularity of the generalized solutions of the equation det(∂ 2 u/∂xi ∂xj ) = ϕ(x1 , x2 , ..., xn ) > 0, Dokl. Akad. Nauk SSSR 200 (1971), 534– 537 (Russian); Engl. transl.: in Soviet Math. Dokl. 12 (1971), 1436–1440.
A.V. Pogorelov, The Dirichlet problem for the multidimensional analogue of the Monge–Ampère equation, Dokl. Akad. Nauk SSSR 201 (1971), 790–793 (Russian); Engl. transl.: Soviet Math. Dokl. 12 (1971), 1227–1231.
A.V. Pogorelov, The Minkowski Multidimensional Problem, Nauka, Moscow, 1975 (Russian); Engl. transl.: Scripta Series in Mathematics, V.H. Winston & Sons, Washington, D.C.; Halsted Press [John Wiley & Sons], New York-Toronto-London, 1978.
