Geodesic
The integral method of barrier functions and the Dirichlet problem for equations with operators of Monge--Amp\`ere type
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 179-192

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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. Bibliography: 7 titles. 
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     author = {N. M. Ivochkina},
     title = {The integral method of barrier functions and the {Dirichlet} problem for equations with operators of {Monge--Amp\`ere} type},
     journal = {Sbornik. Mathematics},
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     volume = {40},
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     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_2_a3/}
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N. M. Ivochkina. The integral method of barrier functions and the Dirichlet problem for equations with operators of Monge--Amp\`ere type. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 179-192. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a3/