Solution of the Dirichlet problem for curvature equations of order $m$

Solvability conditions for curvature equations of order which are sufficient, and almost necessary, are obtained, and theorems concerning the existence of solutions in $C^{l+2+\alpha}(\overline\Omega)$, $l\geqslant2$, $0<\alpha<1$, are proved. The first-order curvature equation coincides with the curvature equation of order $m$, and the curvature equation of order $n$ with the Monge–Ampère equation.
Bibliography: 18 titles.