On the mixed Cauchy problem with data on singular conics

Abstract

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 $Q_{2p}(D)$.

Cited by in corpus (2)

• A Fischer type decomposition theorem from the apolar inner product
• The Goursat problem for a generalized Helmholz operator in the plane