Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bounds for ratios of eigenvalues of the Dirichlet Laplacian


Authors: Mark S. Ashbaugh and Rafael D. Benguria
Journal: Proc. Amer. Math. Soc. 121 (1994), 145-150
MSC: Primary 35P15; Secondary 35J05
MathSciNet review: 1186125
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We use a doubling scheme to derive a bound for the ratio of the $ {2^k}$th eigenvalue to the first for the Dirichlet Laplacian on a bounded domain $ \Omega \subset {\mathbb{R}^n}$. The explicit bounds we obtain derive from the optimal bound $ {({\lambda _2}/{\lambda _1})_\Omega } \leq {({\lambda _2}/{\lambda _1})_{n -{\text{dimensional ball}}}}$ (the Payne-Pólya-Weinberger conjecture) recently proved by us.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35P15, 35J05

Retrieve articles in all journals with MSC: 35P15, 35J05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186125-1
PII: S 0002-9939(1994)1186125-1
Article copyright: © Copyright 1994 American Mathematical Society