Geodesic
On the Dirichlet problem for Bellman's equation in a plane domain
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 231-248 
M. V. Safonov. On the Dirichlet problem for Bellman's equation in a plane domain. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 231-248. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a6/
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     title = {On the {Dirichlet} problem for {Bellman's} equation in a~plane domain},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Dirichlet problem for Bellman's equation in a plane domain is considered. It is shown that, under certain assumptions about the type of smoothness and the “weak” nondegeneracy of the corresponding controlled diffusion process, the solution of this Dirichlet problem is the pay-off function of an optimal control problem. Under supplementary assumptions about smoothness, the pay-off function is also smooth. Bibliography: 11 titles.

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

[3] N. V. Krylov, Lektsii po teorii ellipticheskikh differentsialnykh uravnenii, izd-vo MGU, Moskva, 1972

[4] M. I. Freidlin, “O gladkosti reshenii vyrozhdayuschikhsya ellipticheskikh uravnenii”, Izv. AN SSSR, seriya matem., 32 (1968), 1391–1413 | MR | Zbl

[5] O. A. Ladyzhenskaya, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, izd-vo «Nauka», Moskva, 1964 | MR

[6] I. Ya. Bakelman, Geometricheskie metody resheniya ellipticheskikh uravnenii, izd-vo «Nauka», Moskva, 1965 | MR

[7] Dzh. L. Dub, Veroyatnostnye protsessy, IL, Moskva, 1962

[8] R. Sh. Liptser, A. N. Shiryaev, Statistika sluchainykh protsessov, izd-vo «Nauka», Moskva, 1974 | MR

[9] I. I. Gikhman, A. V. Skorokhod, Stokhasticheskie differentsialnye uravneniya, izd-vo «Naukova dumka », Kiev, 1968 | MR

[10] M. I. Freidlin, “O faktorizatsii neotritsatelno opredelennykh matrits”, Teoriya veroyatn., 13:2 (1968), 375–378 | MR | Zbl

[11] N. V. Krylov, “O edinstvennosti resheniya uravneniya Bellmana”, Izv. AN SSSR, seriya matem., 35 (1971), 1377–1388 | MR | Zbl