Geodesic
On~the first boundary value problem for nonlinear degenerate elliptic equations
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 217-244

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1988_30_2_a1,
     author = {N. V. Krylov},
     title = {On~the first boundary value problem for nonlinear degenerate elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {217--244},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a1/}
}
TY  - JOUR
AU  - N. V. Krylov
TI  - On~the first boundary value problem for nonlinear degenerate elliptic equations
JO  - Izvestiya. Mathematics 
PY  - 1988
SP  - 217
EP  - 244
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a1/
LA  - en
ID  - IM2_1988_30_2_a1
ER  - 
%0 Journal Article
%A N. V. Krylov
%T On~the first boundary value problem for nonlinear degenerate elliptic equations
%J Izvestiya. Mathematics 
%D 1988
%P 217-244
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a1/
%G en
%F IM2_1988_30_2_a1
N. V. Krylov. On~the first boundary value problem for nonlinear degenerate elliptic equations. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 217-244. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a1/