Strong solutions of stochastic equations with singular time dependent drift

@article{Krylov2005StrongSO,
  title={Strong solutions of stochastic equations with singular time dependent drift},
  author={Nicolai V. Krylov and Michael R{\"o}ckner},
  journal={Probability Theory and Related Fields},
  year={2005},
  volume={131},
  pages={154-196}
}
Abstract.We prove existence and uniqueness of strong solutions to stochastic equations in domains with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local Lq_Lp-integrability of b in ℝ×G with d/p+2/q<1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function ψ blowing up as G∋x→∂G, we prove that the conditions 2Dtψ≤Kψ,2Dtψ+Δψ≤Keɛψ,ɛ ∈ [0,2), imply that the explosion time is infinite and the… 
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