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This article is cited in 4 scientific papers (total in 4 papers)
On the first boundary value problem for nonlinear degenerate elliptic equations
N. V. Krylov
Abstract:
This article is devoted to a proof of a general theorem on the existence of a solution of the first boundary value problem for a degenerate Bellman equation. In contrast to other papers the nonlinearity of the equation is used here and leads, for example, to a proof of solvability of the simplest Monge–Ampére equation $\det (u_{xx})=f^d(x)$ for $f \in C^2$, $f\geqslant0$ in a strictly convex region of class $C^3$ with zero data on the boundary.
Bibliography: 18 titles.
Received: 11.04.1985
Citation:
N. V. Krylov, “On the first boundary value problem for nonlinear degenerate elliptic equations”, Math. USSR-Izv., 30:2 (1988), 217–244
Linking options:
https://www.mathnet.ru/eng/im1292https://doi.org/10.1070/IM1988v030n02ABEH001002 https://www.mathnet.ru/eng/im/v51/i2/p242
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Abstract page: | 478 | Russian version PDF: | 131 | English version PDF: | 13 | References: | 51 | First page: | 1 |
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