St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator


Author: N. Filonov
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 2.
Journal: St. Petersburg Math. J. 16 (2005), 413-416
MSC (2000): Primary 35J05, 35P15
Published electronically: March 9, 2005
MathSciNet review: 2068346
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Abstract | References | Similar Articles | Additional Information

Abstract: A simple proof of the inequality $\mu_{k+1} < \lambda_k$ is given. Here the $\lambda_k$ (respectively, $\mu_k$) are the eigenvalues of the Dirichlet (respectively, Neumann) problem for the Laplace operator in an arbitrary domain of finite measure in $\mathbb{R} ^d$, $d>1$.


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Additional Information

N. Filonov
Affiliation: St. Petersburg State University, Physics Department, Ulyanovskaya Ul. 1, Petrodvorets, St. Petersburg 198504, Russia
Email: filonov@mph.phys.spbu.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00857-5
Keywords: Dirichlet problem, Neumann problem, spectrum
Received by editor(s): September 1, 2003
Published electronically: March 9, 2005
Additional Notes: Supported by RFBR (grant no. 02-01-00798).
Dedicated: Dedicated to my teacher Mikhail Shlemovich Birman
Article copyright: © Copyright 2005 American Mathematical Society