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Mosc. Math. J., 2015, Volume 15, Number 1, Pages 101–106 (Mi mmj551)  

This article is cited in 1 scientific paper (total in 1 paper)

Eigenfunctions for $2$-dimensional tori and for rectangles with Neumann boundary conditions

Thomas Hoffmann-Ostenhof

Department of Theoretical Chemistry, A 1090 Wien, Währingerstraße 17, Austria

Abstract: Consider the eigenfunctions u for a 2D-torus, respectively, the free rectangular membrane, so that $-\Delta u=\lambda u$ on $\mathcal R(c,d)=(0,c)\times(0,d)$ with periodic, respectively, Neumann boundary conditions. In this note we show that if $u>0$ on $\partial\mathcal R(c,d)$ then $u\equiv C>0$ in $\mathcal R(c,d)$.

Key words and phrases: eigenfunctions, 2D torus, free rectangular membrane.

DOI: https://doi.org/10.17323/1609-4514-2015-15-1-101-106

Full text: http://www.mathjournals.org/.../2015-015-001-006.html
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Bibliographic databases:

MSC: 35B05, 35J05
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Citation: Thomas Hoffmann-Ostenhof, “Eigenfunctions for $2$-dimensional tori and for rectangles with Neumann boundary conditions”, Mosc. Math. J., 15:1 (2015), 101–106

Citation in format AMSBIB
\Bibitem{Hof15}
\by Thomas~Hoffmann-Ostenhof
\paper Eigenfunctions for $2$-dimensional tori and for rectangles with Neumann boundary conditions
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 1
\pages 101--106
\mathnet{http://mi.mathnet.ru/mmj551}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-1-101-106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427414}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000354886200006}


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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. B. Siudeja, “Nearly radial Neumann eigenfunctions on symmetric domains”, J. Spectr. Theory, 8:3 (2018), 949–969  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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