Geodesic
On the classical solvability of the Dlrichlet problem for the Monge–Ampère equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 4, Tome 131 (1983), pp. 72-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that the problem $\det(u_{xx})=f(x, u, u_x)\geqslant\nu>0$, $u|_{\partial\Omega}=\phi(x)$ is solvable in $C^{k+2+\alpha}(\bar\Omega)$, $k\geqslant2$, $0<\alpha<1$ if the natural connection between $\partial\Omega$-curvature and $|p|$-growth of $f(x, u, p)$ is valid. 
@article{ZNSL_1983_131_a5,
     author = {N. M. Ivochkina},
     title = {On the classical solvability of the {Dlrichlet} problem for the {Monge{\textendash}Amp\`ere} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--79},
     year = {1983},
     volume = {131},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_131_a5/}
}
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N. M. Ivochkina. On the classical solvability of the Dlrichlet problem for the Monge–Ampère equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 4, Tome 131 (1983), pp. 72-79. http://geodesic.mathdoc.fr/item/ZNSL_1983_131_a5/