Open Access
2008 An eigenvalue problem with mixed boundary conditions and trace theorems
Catherine Bandle
Banach J. Math. Anal. 2(2): 68-75 (2008). DOI: 10.15352/bjma/1240336293


An eigenvalue problem is considered where the eigenvalue appears in the domain and on the boundary. This eigenvalue problem has a spectrum of discrete positive and negative eigenvalues. The smallest positive and the largest negative eigenvalue $\lambda_{\pm 1}$ can be characterized by a variational principle. We are mainly interested in obtaining non trivial upper bounds for $\lambda_{-1}$. We prove some domain monotonicity for certain special shapes using a kind of maximum principle derived by C. Bandle, J.v. Bellow and W. Reichel in [J. Eur. Math. Soc., 10 (2007), 73-104]. We then apply these bounds to the trace inequality.


Download Citation

Catherine Bandle. "An eigenvalue problem with mixed boundary conditions and trace theorems." Banach J. Math. Anal. 2 (2) 68 - 75, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1141.35040
MathSciNet: MR2404104
Digital Object Identifier: 10.15352/bjma/1240336293

Primary: 35P15
Secondary: 47A75 , 49R50 , 51M16

Keywords: comparison theorems for eigenvalues , estimates of eigenvalues , trace inequality

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 2 • 2008
Back to Top