Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1141.35040
Bandle, Catherine
An eigenvalue problem with mixed boundary conditions and trace theorems.
(English)
[J] Banach J. Math. Anal. 2, No. 2, 68-75, electronic only (2008). ISSN 1735-8787/e

Summary: 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 {\it C. Bandle}, {\it J. von Bellow} and {\it W. Reichel} in [J. Eur. Math. Soc. (JEMS) 10, No. 1, 73--104 (2008; Zbl 1167.35012)]. We then apply these bounds to the trace inequality.
MSC 2000:
*35P15 Estimation of eigenvalues for PD operators
49R50 Variational methods for eigenvalues of operators
51M16 Inequalities and extremum problems (geometry)

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

Citations: Zbl 1167.35012

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences