The integral method of barrier functions and the Dirichlet problem for equations with operators of Monge–Ampère type

A priori boundedness of the solution of the Dirichlet problem is proved for the equation $F(m;u)=f(x,u,u_x)$, where $F(m;u)$ is the sum of all principal minors of order $m$ in the Hessian $\det(u_{xx})$. The boundedness in question is relative to the $C^2(\Omega)$-norm and is demonstrated by combining the methods of integral inequalities and barrier functions.
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