  We consider a problem of mixed Cauchy type for certain holomorphic partial
differential operators whose principal part $Q_{2p}(D)$ essentially is the
(complex) Laplace operator to a power, $\Delta^p$. We pose inital data on a
singular conic divisor given by P=0, where $P$ is a homogeneous polynomial of
degree $2p$. We show that this problem is uniquely solvable if the polynomial
$P$ is elliptic, in a certain sense, with respect to the principal part
$Q_{2p}(D)$.
