Geodesic
Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation
Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 319-326 
N. V. Efimov. Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation. Sbornik. Mathematics, Tome 29 (1976) no. 3, pp. 319-326. http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/
@article{SM_1976_29_3_a1,
     author = {N. V. Efimov},
     title = {Estimates for the dimensions of the domains of regularity of solutions of certain {Monge{\textendash}Amp\`ere} equation},
     journal = {Sbornik. Mathematics},
     pages = {319--326},
     year = {1976},
     volume = {29},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/}
}
TY  - JOUR
AU  - N. V. Efimov
TI  - Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 319
EP  - 326
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/
LA  - en
ID  - SM_1976_29_3_a1
ER  - 
%0 Journal Article
%A N. V. Efimov
%T Estimates for the dimensions of the domains of regularity of solutions of certain Monge–Ampère equation
%J Sbornik. Mathematics
%D 1976
%P 319-326
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1976_29_3_a1/
%G en
%F SM_1976_29_3_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

An (incomplete) Monge-Ampère equation is considered, as well as a domain where this equation has a regular solution. Estimates are established on the size of a rectangle that can be inscribed in this domain. The estimates depend on the equation, but not on its solution. Bibliography: 3 titles.

[1] N. V. Efimov, “Issledovanie polnoi poverkhnosti otritsatelnoi krivizny”, DAN SSSR, 93:3 (1953), 393–395 | MR | Zbl

[2] N. V. Efimov, “Issledovanie odnoznachnoi proektsii poverkhnosti otritsatelnoi krivizny”, DAN SSSR, 93:4 (1953), 609–611 | MR | Zbl

[3] E. Heinz, “Über Flächen mit eineindeutiger Projektion auf eine Ebene, deren Krümmungen durch Ungleichungen eingeschränkt sind”, Math. Ann., 129:5 (1955), 451–454 | DOI | MR | Zbl