Abstract
One considers Bellman's elliptic equation with constant coefficients and zero boundary values on a plane part of the boundary. In this case one gives a simplified proof of N. V. Krylov's result regarding the boundary estimates of the Hölder constants of the second derivatives of the solutions of the Bellman equation.
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Literature cited
M. V. Safonov, “On the classical solution of Bellman's elliptic equation,” Dokl. Akad. Nauk SSSR,278, No. 4, 810–813 (1984).
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 3, 487–523 (1982).
L. C. Evans, “Classical solutions of fully nonlinear, convex, second-order elliptic equations,” Commun. Pure Appl. Math.,35, 333–363 (1982).
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations in a domain,” Izv. Akad. Nauk SSSR, Ser. Mat.,47, No. 1, 75–108 (1983).
M. V. Savonov, “Boundary estimates in e+α for the solutions of nonlinear elliptic equations,” Usp. Mat. Nauk,38, No. 5, 146–147 (1983).
O. A. Ladyzhenskaya and N. N. Ural'tseva, “Estimates at the boundary of the domain of the Hölder norm of the derivatives of the solutions of quasilinear elliptic and parabolic equations of the general form,” Preprint LOMI R-1-85, Leningrad (1985).
N. V. Krylov and M. V. Safonov, “A certain property of the solutions of parabolic equations with measurable coefficients,” Izv. Akad. Nauk SSSR, Ser. Mat.,44, No. 1, 161–175 (1980).
M. V. Safonov, “Harnack's inequality for elliptic equations and the Hölder property of their solutions,” J. Sov. Math.,21, No. 5 (1983).
L. Bers, F. John, and M. Schechter, Partial Differential Equations, Amer. Math. Soc., Providence (1964).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 150–154, 1985.
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Safonov, M.V. Smoothness near the boundary of the solutions of the elliptic Bellman equations. J Math Sci 37, 885–888 (1987). https://doi.org/10.1007/BF01387728
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DOI: https://doi.org/10.1007/BF01387728