We consider a problem of mixed Cauchy type for certain holomorphic partial differential
operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to
a power, Δp. We provide 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 Q2p(D).
