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Journal of the London Mathematical Society Advance Access originally published online on June 2, 2008
Journal of the London Mathematical Society 2008 78(1):248-266; doi:10.1112/jlms/jdn028
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© 2008 London Mathematical Society

On the mixed Cauchy problem with data on singular conics

Peter Ebenfelt

Department of Mathematics
University of California
San Diego
La Jolla, CA 92093–0112
USA

Hermann Render

Departamento de Matemáticas y Computación
Universidad de la Rioja
Edificio Vives
Luis de Ulloa s/n.
26004 Logroño
Spain
render@gmx.de

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, {Delta}p. 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).

2000 Mathematics Subject Classification 35A10, 35J05.

The first author is supported in part by DMS-0401215. The second author is supported in part by Grant BFM2003-06335-C03-03 of the D.G.I. of Spain.

Received November 27, 2006; revised March 12, 2008; published online June 2, 2008.


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