Citation
D. Bucur et A. Henrot, Minimization of the third eigenvalue of the Dirichlet Laplacian, P ROY SOC A, 456(1996), 2000, pp. 985-996
Citations number
23
Categorie Soggetti
Multidisciplinary
Journal title
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
ISSN journal
13645021
→ ACNP
Volume
456
Issue
1996
Year of publication
2000
Pages
985 - 996
Database
ISI
SICI code
1364-5021(20000408)456:1996<985:MOTTEO>2.0.ZU;2-5
Abstract
In this paper, we prove the existence of a domain which minimizes the third
Dirichlet eigenvalue lambda(3) of the Laplacian (-Delta) in the family of
domains of R-N of given volume. Some remarks are made on the existence of a
minimizer for lambda(k), k greater than or equal to 4 in the same family,
and for a class of functionals depending on (lambda(1):lambda(2)).