Geodesic
On the Dirichlet problem for Bellman's equation in a~plane domain
Sbornik. Mathematics, Tome 34 (1978) no. 4, pp. 521-526

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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. 
@article{SM_1978_34_4_a6,
     author = {M. V. Safonov},
     title = {On the {Dirichlet} problem for {Bellman's} equation in a~plane domain},
     journal = {Sbornik. Mathematics},
     pages = {521--526},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_4_a6/}
}
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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/