Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Author: N. V. Krylov
Journal: Trans. Amer. Math. Soc. 374 (2021), 2805-2822
MSC (2020): Primary 35K10, 35J15, 60J60
DOI: https://doi.org/10.1090/tran/8282
Published electronically: January 20, 2021
MathSciNet review: 4223034
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 35K10, 35J15, 60J60

Retrieve articles in all journals with MSC (2020): 35K10, 35J15, 60J60


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
Article copyright: © Copyright 2021 American Mathematical Society