The Goursat problem for a generalized Helmholz operator in the plane
Analysis of PDEs
2007-05-23 v1 Complex Variables
Abstract
We consider the Goursat problem in the plane for partial differential operators whose principal part is the th power of the standard Laplace operator. The data is posed on a union of 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.
Cite
@article{arxiv.math/0703111,
title = {The Goursat problem for a generalized Helmholz operator in the plane},
author = {Peter Ebenfelt and Hermann Render},
journal= {arXiv preprint arXiv:math/0703111},
year = {2007}
}