On an inequality between Dirichlet and Neumann eigenvalues for the Laplace operator
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N. Filonov
Translated by: the author - St. Petersburg Math. J. 16 (2005), 413-416
- DOI: https://doi.org/10.1090/S1061-0022-05-00857-5
- Published electronically: March 9, 2005
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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 $\mathbb {R}^d$, $d>1$.References
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Bibliographic Information
- N. Filonov
- Affiliation: St. Petersburg State University, Physics Department, Ulyanovskaya Ul. 1, Petrodvorets, St. Petersburg 198504, Russia
- MR Author ID: 609754
- Email: filonov@mph.phys.spbu.ru
- Received by editor(s): September 1, 2003
- Published electronically: March 9, 2005
- Additional Notes: Supported by RFBR (grant no. 02-01-00798).
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 413-416
- MSC (2000): Primary 35J05, 35P15
- DOI: https://doi.org/10.1090/S1061-0022-05-00857-5
- MathSciNet review: 2068346
Dedicated: Dedicated to my teacher Mikhail Shlemovich Birman