Abstract
We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth 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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The first author is supported in part by DMS-0401215.
The second author is supported in part by Grant MTM2006-13000-C03-03 of the D.G.I. of Spain.
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Ebenfelt, P., Render, H. The Goursat problem for a generalized Helmholtz operator in the plane. J Anal Math 105, 149–167 (2008). https://doi.org/10.1007/s11854-008-0033-5
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DOI: https://doi.org/10.1007/s11854-008-0033-5