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In this paper we present a weighted $L_p$-theory of second-order parabolicpartial differential equations defined on $C^1$ domains. The leadingcoefficients are assumed to be measurable in time variable and have VMO(vanishing mean oscillation) or small BMO (bounded mean oscillation) withrespect to space variables, and lower order coefficients are allowed to beunbounded and to blow up near the boundary.  Our BMO condition is slightly relaxed than the others in the literature.

A weighted $L_p$-theory for parabolic PDEs with BMO coefficients on $C^1$-domains