Strong solutions of stochastic equations with singular time dependent drift

We prove existence and uniqueness of strong solutions to stochastic equations in domains G [is a proper subset] [set of real numbers] with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local Lq_Lp-integrability of b in [set of real numbers xG with d/p+2/q [is less than] 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function [psi] blowing up as G[reversed epsilon] x[arrow pointing right]aG, we prove that the conditions 2Dt[psi][is less than or equal to]K[psi],2Dt[psi]+[delta][psi][is less than or equal to] Ke ^super epsilon^^super psi^, epsilon}e[0,2) imply that the explosion time is infinite and the distributions of the solution have sub Gaussian tails. [PUBLICATION ABSTRACT]