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Mosc. Math. J., 2004, Volume 4, Number 2, Pages 369–375 (Mi mmj153)  

This article is cited in 3 scientific papers (total in 3 papers)

Remarks on the membrane and buckling eigenvalues for planar domains

L. Friendland

University of Arizona, Department of Mathematics

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.

Full text: http://www.ams.org/.../abst4-2-2004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 35P15, 47A55, 47F05
Received: August 6, 2003
Language: English

Citation: L. Friendland, “Remarks on the membrane and buckling eigenvalues for planar domains”, Mosc. Math. J., 4:2 (2004), 369–375

Citation in format AMSBIB
\Bibitem{Fri04}
\by L.~Friendland
\paper Remarks on the membrane and buckling eigenvalues for planar domains
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 2
\pages 369--375
\mathnet{http://mi.mathnet.ru/mmj153}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2108442}
\zmath{https://zbmath.org/?q=an:1072.35134}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kelliher J.P., “Eigenvalues of the Stokes Operator Versus the Dirichlet Laplacian in the Plane”, Pacific Journal of Mathematics, 244:1 (2010), 99–132  crossref  mathscinet  zmath  isi  scopus
    2. Gazzola F., Grunau H.-Ch., Sweers G., “Models of Higher Order”, Polyharmonic Boundary Value Problems, Lecture Notes in Mathematics, 1991, 2010, 1  crossref  mathscinet  isi  scopus
    3. Antunes P.R.S., “On the buckling eigenvalue problem”, Journal of Physics A-Mathematical and Theoretical, 44:21 (2011), 215205  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Moscow Mathematical Journal
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