Elliptic equations with VMO a, b$\in L_{d}$, and c$\in L_{d/2}$
Nicolai V. Krylov · Transactions of the American Mathematical Society · 2020
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, $1 0$. Weak uniqueness of the martingale problem associated with such operators is also obtained.