Geodesic
A priori estimates for solutions of nonlinear second-order elliptic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 31-59 
A. V. Ivanov. A priori estimates for solutions of nonlinear second-order elliptic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 31-59. http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a2/
@article{ZNSL_1976_59_a2,
     author = {A. V. Ivanov},
     title = {A priori estimates for solutions of nonlinear second-order elliptic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--59},
     year = {1976},
     volume = {59},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a2/}
}
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TI  - A priori estimates for solutions of nonlinear second-order elliptic equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1976
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VL  - 59
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a2/
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%U http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a2/
%G ru
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider classes of elliptic equations of the form $F(x,u,\Delta u,D^2u)=0$ for the solutions of which one establishes local and global a priori estimates for $|D^2u|=(\sum_{ij}u^2_{x_ix_j})^{1/2}$ and $|D^3u|=(\sum_{ijk}u^2_{x_ix_jx_k})^{1/2}$. In particular, one investigates the Monge-Ampere equation $\det\|u_{x_ix_j}\|=f(x)$, $f(x)>0$ and for its convex solutions one constructs a local $|D^2u|$ and a global estimate for $\|D^3u\|_{L^2}$ and a local estimate for.