The Dirichlet problem in the unit ball is considered for the strictly elliptic operator
L
=
∑
a
i
j
D
i
j
L = \sum {{a_{ij}}{D_{ij}}}
, where the
a
i
j
{a_{ij}}
, are smooth away from the origin and radially homogeneous:
a
i
j
(
r
x
)
=
a
i
j
(
x
)
,
r
>
0
,
x
≠
0
{a_{ij}}(rx) = {a_{ij}}(x),\;r > 0,\;x \ne 0
. Existence and uniqueness are proved for solutions in a certain space of functions. Necessary and sufficient conditions are given for an extended maximum principle to hold.