Geodesic
On conditions of solvability of the Dirichlet problem for $m$-curvature equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 66-74

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The paper contains the ensharpened variant of the Jenkins–Serrin–Trudinger condition relating to the Dirichlet problem for curvature equations. New condition provides the classical solvability to the Hauss curvature equation in the case of positive curvature, which sufficiently small on the boundary. Bibliography: 8 titles. 
@article{ZNSL_1994_213_a3,
     author = {N. M. Ivochkina},
     title = {On conditions of solvability of the {Dirichlet} problem for $m$-curvature equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--74},
     publisher = {mathdoc},
     volume = {213},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a3/}
}
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N. M. Ivochkina. On conditions of solvability of the Dirichlet problem for $m$-curvature equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 66-74. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a3/