Estimates in $L_{p}$ for solutions of SPDEs with coefficients in Morrey classes

Abstract

For solutions of a certain class of SPDEs in divergence form we present some estimates of their $L_{p}$-norms and the $L_{p}$-norms of their first-order derivatives. The main novelty is that the low-order coefficients are supposed to belong to certain Morrey classes instead of $L_{p}$-spaces. Our results are new even if there are no stochastic terms in the equation.