ON DIVERGENCE FORM SPDES WITH GROWING COEFFICIENTS IN W12 SPACES WITHOUT WEIGHTS

摘要

We consider divergence form uniformly parabolic stochastic partial differential equations 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.