关于六阶超定边值问题的Payne-Schaefer猜想
On Payne-Schaefer's Conjecture about an Overdetermined Boundary Problem of Sixth Order
摘要：
本文考虑超定边值问题。首先，我们在二维情形下证明了关于六阶超定问题的Payne-Schaefer猜想，并对维数不小于小于3的情形给出了一个附加条件.其次，我们证明了一个四阶超定问题的积分恒等式，该恒等式可用于推导Bennett对称性定理。最后，利用积分恒等式证明了一个二阶超定问题的对称性结果。
英文摘要：
This paper considers overdetermined boundary problems. Firstly, we give a proof to the Payne-Schaefer conjecture about an overdetermined problem of sixth order in the two dimensional case and under an additional condition for the case of dimension no less than three. Secondly, we prove an integral identity for an overdetermined problem of fourth order which can be used to deduce Bennett's symmetry theorem. Finally, we prove a symmetry result for an overdetermined problem of second order by integral identities.
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。
