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