## Elliptic equations with VMO a, b$\,\in L_{d}$, and c$\,\in L_{d/2}$

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- by N. V. Krylov PDF
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**374**(2021), 2805-2822 Request permission

## Abstract:

We consider elliptic equations with operators $L=a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b\in L_{d}$ and $c\in L_{q}$, $c\geq 0$, $d>q\geq d/2$. We prove the solvability of $Lu=f\in L_{p}$ in bounded $C^{1,1}$-domains, $1<p\leq q$, 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 obtained.## References

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## Additional Information

**N. V. Krylov**- Affiliation: Department of Mathematics, 127 Vincent Hall, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 189683
- Email: nkrylov@umn.edu
- Received by editor(s): March 24, 2020
- Received by editor(s) in revised form: August 8, 2020
- Published electronically: January 20, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 2805-2822 - MSC (2020): Primary 35K10, 35J15, 60J60
- DOI: https://doi.org/10.1090/tran/8282
- MathSciNet review: 4223034