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Symmetry theorems for the overdetermined eigenvalue problems
- Source :
-
Journal of Differential Equations . Feb2007, Vol. 233 Issue 2, p585-600. 16p. - Publication Year :
- 2007
-
Abstract
- Abstract: The well-known Schiffer conjecture saying that for a smooth bounded domain , if there exists a positive Neumann eigenvalue such that the corresponding Neumann eigenfunction u is constant on the boundary of Ω, then Ω is a ball. In this paper, we shall prove that the Schiffer conjecture holds if and only if the third order interior normal derivative of the corresponding Neumann eigenfunction is constant on the boundary. We also prove a similar result to the Berenstein conjecture for the overdetermined Dirichlet eigenvalue problem. [Copyright &y& Elsevier]
- Subjects :
- *MATRICES (Mathematics)
*ALGEBRA
*MATHEMATICAL analysis
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 233
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 23443919
- Full Text :
- https://doi.org/10.1016/j.jde.2006.08.020