On the Payne-Schaefer Conjecture About an Overdetermined Boundary Problem of Sixth Order

Abstract

This paper considers overdetermined boundary problems. Firstly, the author gives a proof of 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, the author proves an integral identity for an overdetermined problem of fourth order which can be used to deduce Bennett’s symmetry theorem. Finally, the author proves a symmetry result for an overdetermined problem of second order by integral identities.

Keywords

Overdetermined problem / Payne-Schaefer conjecture / Bennett theorem / Euclidean ball / 35N25 / 35N30 / 35R01

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