Geodesic
On the limit passage in parabolic Bellman equations
Izvestiya. Mathematics, Tome 13 (1979) no. 3, pp. 677-684 
N. V. Krylov. On the limit passage in parabolic Bellman equations. Izvestiya. Mathematics, Tome 13 (1979) no. 3, pp. 677-684. http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a6/
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     author = {N. V. Krylov},
     title = {On the limit passage in parabolic {Bellman} equations},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper contains theorems on passing to the limit under the sign of a nonlinear parabolic operator of minimax type, when a certain convergence of a sequence of functions is assumed, but the convergence of the derivatives of these functions is not assumed. The functions under consideration belong to Sobolev classes. Bibliography: 7 titles.

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

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

[3] Krylov N. V., “K teorii nelineinykh vyrozhdayuschikhsya ellipticheskikh uravnenii”, Dokl. AN SSSR, 201:6 (1971), 1279–1281

[4] Danford N., Shvarts Dzh. T., Lineinye operatory, obschaya teoriya, IL, M., 1962

[5] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[6] Krylov N. V., “O printsipe maksimuma dlya nelineinykh parabolicheskikh i ellipticheskikh uravnenii”, Izv. AN SSSR. Ser. matem., 42 (1978), 1050–1062 | MR | Zbl

[7] Krylov N. V., “Ogranichenno neodnorodnye ellipticheskie i parabolicheskie uravneniya na ploskosti”, Matem. sbornik, 82:1 (1970), 99–110 | MR | Zbl