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The Goursat problem for a generalized Helmholz operator in the plane

Peter Ebenfelt·Hermann Render
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Abstract

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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Peter Ebenfelt, Hermann Render. 2007-03-04. The Goursat problem for a generalized Helmholz operator in the plane. https://arxiv.org/abs/math/0703111

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