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| On the Payne-Schaefer Conjecture About an Overdetermined Boundary Problem of Sixth Order |
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Citation： |
Changyu XIA.On the Payne-Schaefer Conjecture About an Overdetermined Boundary Problem of Sixth Order[J].Chinese Annals of Mathematics B,2026,(1):213~228 |
| Page view： 202
Net amount： 106 |
Authors： |
Changyu XIA; |
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| Abstract： |
This paper considers overdetermined boundary value problems for sixth-order elliptic equations. The author gives a complete proof of the Payne–Schaefer conjecture, which asserts that if a solution to a certain sixth-order equation satisfies two homogeneous boundary conditions on a smooth domain, then the domain must be a ball. The proof relies on integral identities, the Bennett identity, and a moving plane argument. |
Keywords： |
Overdetermined problem Payne-Schaefer conjecture Bennett theorem Euclidean ball |
Classification： |
35N25, 35N30, 35R01 |
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