Elliptic equations in Sobolev spaces with Morrey drift and the zeroth-order coefficients

Krylov, N.

doi:10.1090/tran/8982

Elliptic equations in Sobolev spaces with Morrey drift and the zeroth-order coefficients
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by N. V. Krylov;

Trans. Amer. Math. Soc. 376 (2023), 7329-7351

DOI: https://doi.org/10.1090/tran/8982

Published electronically: July 17, 2023

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Abstract:

We consider elliptic equations with operators $L=a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b$ in a Morrey class containing $L_{d}$, and $c\geq 0$ in a Morrey class containing $L_{d/2}$. We prove the solvability in Sobolev spaces of $Lu=f\in L_{p}$ in bounded $C^{1,1}$-domains, and of $\lambda u-Lu=f$ in the whole space for any $\lambda >0$. Weak uniqueness of the martingale problem associated with such operators is also discussed.

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