Geodesic
Estimates for solutions of quasilinear elliptic equations connected with problems of geometry “in the large”
Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 348-363 
I. Ya. Bakelman; B. E. Kantor. Estimates for solutions of quasilinear elliptic equations connected with problems of geometry “in the large”. Sbornik. Mathematics, Tome 20 (1973) no. 3, pp. 348-363. http://geodesic.mathdoc.fr/item/SM_1973_20_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following questions are presented in this paper. 1. A geometric method for obtaining two-sided estimates for general quasilinear elliptic equations and its applications to problems of the calculus of variations and the problem of recovering a hypersurface from its mean curvature in spaces of constant curvature. 2. Estimates of the modulus of the gradient for a hypersurface with boundary in a Riemannian space by means of its mean curvature and the metric tensor of the space. 3. Estimates of the modulus of the gradient of a hypersurface depending on the distance of a point from the boundary and its mean curvature in Euclidean space. Estimates of these three types are of independent interest and play a fundamental role in the proofs of existence theorems for a hypersurface with prescribed mean curvature in Riemannian spaces. Bibliography: 3 titles.

[1] I. Ya. Bakelman, “Giperpoverkhnosti s dannoi srednei kriviznoi i kvazilineinye ellipticheskie uravneniya s silnymi nelineinostyami”, Matem. sb., 75 (117) (1968), 604–638 | MR

[2] I. Ya. Bakelman, “Geometricheskie voprosy kvazilineinykh ellipticheskikh uravnenii”, Uspekhi matem. nauk, XXV:3 (153) (1970), 49–112 | MR

[3] S. Khelgason, Differentsialnaya geometriya i simmetricheskie prostranstva, izd-vo «Mir», Moskva, 1964