Abstract:
Solvability conditions for curvature equations of order which are sufficient, and almost necessary, are obtained, and theorems concerning the existence of solutions in Cl+2+α(¯Ω), l⩾2, 0<α<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.
\Bibitem{Ivo89}
\by N.~M.~Ivochkina
\paper Solution of the Dirichlet problem for curvature equations of order~$m$
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 2
\pages 317--339
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\crossref{https://doi.org/10.1070/SM1990v067n02ABEH002089}
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