On the mixed Cauchy problem with data on singular conics

摘要

We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators with the principal part Q_2p(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 Q_2p(D).