Sobolev space theory of SPDEs with continuous or measurable leading coefficients

We study stochastic partial differential equations with variable coefficients defined on Rd,R+d and bounded C1C1 domains. For equations with continuous leading coefficients we give existence and uniqueness results in Lq(Lp)Lq(Lp)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in LpLp-spaces.