Geodesic
On the classical solvability of the Dlrichlet problem for the Monge--Amp\`ere equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 4, Tome 131 (1983), pp. 72-79

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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 $C^{k+2+\alpha}(\bar\Omega)$, $k\geqslant2$, $0\alpha1$ if the natural connection between $\partial\Omega$-curvature and $|p|$-growth of $f(x, u, p)$ is valid. 
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     author = {N. M. Ivochkina},
     title = {On the classical solvability of the {Dlrichlet} problem for the {Monge--Amp\`ere} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--79},
     publisher = {mathdoc},
     volume = {131},
     year = {1983},
     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--Amp\`ere 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/