A weighted Lp-theory for parabolic PDEs with BMO coefficients on C1-domains

In this paper we present a weighted Lp-theory of second-order parabolic partial differential equations defined on C1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.