Geodesic
On stochastic equations with degenerate diffusion with respect to some of the variables
Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 173-180.

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In this paper the author establishes sufficient existence and uniqueness conditions for a strong solution of Itǒ's stochastic equation with nonsmooth drift under conditions of possible degeneracy of the diffusion with respect to some of the variables. The conditions thus found assume additional smoothness of the coefficients in the direction of the degeneracy. Bibliography: 13 titles. 
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A. Yu. Veretennikov. On stochastic equations with degenerate diffusion with respect to some of the variables. Izvestiya. Mathematics , Tome 22 (1984) no. 1, pp. 173-180. http://geodesic.mathdoc.fr/item/IM2_1984_22_1_a5/

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[7] Yamada T., Watanabe S., “On the uniqueness of solutions of stochastic differential equations, I”, J. Math. Kyoto Univ., 11:1 (1971), 155–167 | MR | Zbl

[8] Veretennikov A. Yu., “O silnykh resheniyakh i yavnykh formulakh dlya reshenii stokhasticheskikh integralnykh uravnenii”, Matem. sb., 111:3 (1980), 434–452 | MR | Zbl

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[10] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

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