On~the first boundary value problem for nonlinear degenerate elliptic equations

N. V. Krylov

Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 217-244.

Résumé

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.

Bibliographie

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