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

N. V. Krylov

paper

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

arXiv:2311.03238

Abstract

We consider parabolic equations with operators $L = \partial_{t} + a^{ij} D_{ij} + b^{i} D_{i} - c$ 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 $L u = f \in L_{p}$ in bounded $C^{1, 1}$ -cylinders.

16 pages