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

N. V. Krylov

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arXiv · 2311.03238

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

N. V. Krylov

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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.

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N. V. Krylov. 2023-11-06. On parabolic equations in Sobolev spaces with lower-order coefficients from Morrey spaces. https://arxiv.org/abs/2311.03238

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