On parabolic equations in Sobolev spaces with lower-order coefficients from Morrey spaces

Abstract

We consider parabolic equations with operators $\mathcal{L}={\partial }_t+a^{ij}{D}_{ij}+b^i{D}_i-c$ with $a$ being almost in VMO, $b$ in a Morrey class containing $L_{d+2}$ and $c$ in a Morrey class containing $L_{(d+2)/2}$. We prove the solvability in Sobolev spaces of $\mathcal{L}u=f\in L_p$ in bounded $C^{1,1}$-cylinders.