Rellich type identities for eigenvalue problems and application to the Pompeiu problem

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Abstract

For classical Neumann eigenvalue, buckling eigenvalue and clamped plate eigenvalue, we give the corresponding Rellich type identities. As an application of these results, then, we obtain a new necessary and sufficient condition for a domain without the Pompeiu property.

Keywords

Rellich's identity
Neumann eigenvalue
Buckling eigenvalue
Clamped plate eigenvalue
The Pompeiu problem
The Schiffer conjecture

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