  We prove the Lp,q-solvability of parabolic equations in divergence form with
full lower-order terms. The coefficients and non-homogeneous terms belong to
mixed Lebesgue spaces with the lowest integrability conditions. In particular,
the coefficients for the lower-order terms are not necessarily bounded. We
study both the Dirichlet and conormal derivative boundary value problems on
irregular domains. We also prove embedding results for parabolic Sobolev
spaces, the proof of which is of independent interest.
