Geodesic
On the Dirichlet problem for Bellman's equation in a plane domain
Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 521-526 
M. V. Safonov. On the Dirichlet problem for Bellman's equation in a plane domain. Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 521-526. http://geodesic.mathdoc.fr/item/SM_1978_34_4_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 proved that under certain restrictions regarding smoothness, “weak” nondegeneracy, and nondegeneracy along the normal to the boundary of the domain this problem has a generalized solution. Under additional conditions regarding smoothness the solution is also smooth. Bibliography: 2 titles.

[1] M. V. Safonov, “O zadache Dirikhle dlya uravneniya Bellmana v ploskoi oblasti”, Matem. sb., 102(144) (1977), 260–279 | MR | Zbl

[2] 0. A. Oleinik, E. V. Radkevich, Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, Itogi nauki. Matem. analiz 1969, VINITI, Moskva, 1971 | MR | Zbl