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.

16 pages