Existence and uniqueness theorems are presented for evolutional stochastic partial differential equations of second order in $L_p$-spaces with weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to space and time variables to be different.
N. Krylov. "SPDEs in $L_q( ( 0,\tau ] , L_p)$ Spaces." Electron. J. Probab. 5 1 - 29, 2000. https://doi.org/10.1214/EJP.v5-69