平面上广义Helmholz算子的Goursat问题
The Goursat problem for a generalized Helmholz operator in the plane
摘要：
本文研究了以标准Laplace算子的$p$次幂为主部的偏微分算子在平面上的Goursat问题。数据放置在通过原点的$2p$不同线的并集上。我们表明，这个Goursat问题的可解性取决于丢番图性质的几何线上的数据构成。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
