The Goursat problem for a generalized Helmholz operator in the plane

Details The Goursat problem for a generalized Helmholz operator in the plane The Goursat problem for a generalized Helmholz operator in the plane

2007-03-04

arxiv.org/abs/math/0703111v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the Goursat problem in the plane for partial differential
operators whose principal part is the $p$th power of the standard Laplace
operator. The data is posed on a union of $2p$ distinct lines through the
origin. We show that the solvability of this Goursat problem depends on
Diophantine properties of the geometry of lines on which the data is posed.

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