Geodesic
On degenerate nonlinear elliptic equations. II
Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 207-228 Cet article a éte moissonné depuis la source Math-Net.Ru

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Dirichlet problems for degenerate nonlinear elliptic equations of Bellman type $\inf_p(L(p)u+f(p))=0$ are studied, where $L(p)$ is a linear elliptic operator of second order. Under certain conditions on the coefficients of $L(p)$, it is shown that this problem is solvable in the class of functions with bounded second derivatives. Bibliography: 15 titles. 
@article{SM_1984_49_1_a12,
     author = {N. V. Krylov},
     title = {On degenerate nonlinear elliptic {equations.~II}},
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     year = {1984},
     volume = {49},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_1_a12/}
}
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N. V. Krylov. On degenerate nonlinear elliptic equations. II. Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 207-228. http://geodesic.mathdoc.fr/item/SM_1984_49_1_a12/

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[3] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

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[6] Krylov N. V., “O predelnom perekhode v vyrozhdennykh uravneniyakh Bellmana. II”, Matem. sb., 107(149) (1978), 56–68 | MR | Zbl

[7] Krylov N. V., “Ob upravlyaemykh diffuzionnykh protsessakh s neogranichennymi koeffitsientami”, Izv. AN SSSR. Seriya matem., 45 (1981), 734–759 | MR | Zbl

[8] Lions P. L., “Control of diffusion in $R^N$”, Comm. Pure and Appl. Math., 34 (1981), 121–147 | DOI | MR | Zbl

[9] Lions P. L., “Equations de Hamilton–Jacobi–Bellman dégénérées”, C. r. Acad. sci., 289, série A (1979), 329–332 | MR | Zbl

[10] Krylov N. V., “Ob upravlenii diffuzionnym protsessom do momenta pervogo vykhoda iz oblasti”, Izv. AN SSSR. Seriya matem., 45 (1981), 1030–1048

[11] Krylov N. V., “Ob upravlenii resheniem stokhasticheskogo integralnogo uravneniya, pri nalichii vyrozhdeniya”, Izv. AN SSSR. Seriya matem., 36 (1972), 248–261 | Zbl

[12] Krylov N. V., “Ob uravnenii Bellmana”, Trudy shkoly-seminara po teoriya sluchainykh protsessov, I (Druskininkai, 1974 g.), Vilnyus, 1975, 202–235

[13] Oleinik O. A., Radkevich E. V., “Uravnenie vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Matem. analiz, 1969, 8, VINITI, M., 1971, 7–252 | MR | Zbl

[14] Genis I. L., Krylov N. V., “Primer odnomernogo upravlyaemogo protsessa”, Teoriya veroyatn., 21:1 (1976), 147–151 | MR | Zbl

[15] Pogorelov A. V., Ob uravneniyakh Monzha–Ampera ellipticheskogo tipa, Izd-vo KhGU, 1960