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

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• 作者：Genqian Liu
• 关键词：Rellich's identity ; Neumann eigenvalue ; Buckling eigenvalue ; Clamped plate eigenvalue ; The Pompeiu problem ; The Schiffer conjecture
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2007
• 出版时间：15 June 2007
• 年：2007
• 卷：330
• 期：2
• 页码：963-975
• 全文大小：152 K

文摘

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.