Advanced Search

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]