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

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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. 
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     author = {I. Ya. Bakelman and B. E. Kantor},
     title = {Estimates for solutions of quasilinear elliptic equations connected with problems of geometry ``in the large''},
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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/