On the mixed Cauchy problem with data on singular conics

Details On the mixed Cauchy problem with data on singular conics On the mixed Cauchy problem with data on singular conics

2007-03-04

arxiv.org/abs/math/0703110v1

Mathematics

Analysis of PDEs

Scientific paper

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 $Q_{2p}(D)$.

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