On divergence form SPDEs with growing coefficients in $W^{1}_{2}$ spaces without weights

Abstract

We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.