Abstract
A local estimate for the second-order solutions to the curvature-type equations is established. Bibliography: 9 titles.
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References
N. M. Ivochkina, “A description of the stability cones generated by differential operators of Monge—Ampere type,”Math. USSR Sb.,50, 259–268 (1985).
N. S. Trudinger, “The Dirichlet problem for the prescribed curvature equation,”Arch. Rat. Mech. Anal.,111, No. 2, 153–179 (1990).
G. V. Yakunina, “Interior estimate for the gradient of a solution to the Dirichlet problem for a curvature-type equation,”Probl. Mat. Anal.,14, 188–196 (1996).
N. S. Trudinger, “Fully nonlinear, uniformly elliptic equations under natural structure conditions,”Trans. Amer. Math. Soc.,278, No. 2, 751–769 (1983).
N. M. Ivochkina and S. I. Prokofieva, “A priori estimate for the second-order derivatives of solutions to the Dirichlet problem for fully nonlinear parabolic equations,”Probl. Mat. Anal.,16, 112–133 (1997).
D. Gilbarg and N. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer, Berlin (1977).
T. Motzkin and W. Wasow, “On the approximation of linear elliptic differential equations by difference equations with positive coefficients,”J. Math. Phys.,31, 253–259 (1953).
O. A. Ladyzhenskaya and N. N. Ural'tseva,Linear and Quasilinear Equations of Elliptic Type, Moscow (1973).
M. V. Safonov,Boundary Value Problems for Nonlinear Second-Order Elliptic and Parabolic Equations, Doctoral Dissertation [in Russian], Leningrad (1988).
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Translated fromProblemy Matematicheskogo Analiza. No. 16. 1997, pp. 134–144.
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Ivochkina, N.M., Yakunina, G.V. Estimate for the second-order derivatives of solutions of curvature-type equations. J Math Sci 92, 4316–4323 (1998). https://doi.org/10.1007/BF02433438
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DOI: https://doi.org/10.1007/BF02433438