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Moscow Mathematical Journal, 2004, Volume 4, Number 2, Pages 369–375
DOI: https://doi.org/10.17323/1609-4514-2004-4-2-369-375 (Mi mmj153) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Remarks on the membrane and buckling eigenvalues for planar domains

L. Friendlander

University of Arizona, Department of Mathematics
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DOI: https://doi.org/10.17323/1609-4514-2004-4-2-369-375
Abstract: I present a counter-example to the conjecture that the first eigenvalue of the clamped buckling problem in a planar domain is not smaller than the third eigenvalue of the fixed membrane in that domain. I also prove that the conjecture holds for domains that are invariant under rotation by angle $\pi/2$.
Key words and phrases: Eigenvalue inequalities, small eigenvalues, buckling problem.
Received: August 6, 2003
Bibliographic databases:
Document Type: Article
MSC: 35P15, 47A55, 47F05
Language: English
Citation: L. Friendlander, “Remarks on the membrane and buckling eigenvalues for planar domains”, Mosc. Math. J., 4:2 (2004), 369–375
Citation in format AMSBIB
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\by L.~Friendlander
\paper Remarks on the membrane and buckling eigenvalues for planar domains
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 2
\pages 369--375
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2108442}
\zmath{https://zbmath.org/?q=an:1072.35134}
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    • This publication is cited in the following 7 articles:
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