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Mat. Sb., 2013, Volume 204, Number 4, Pages 79–102 (Mi msb8106)  

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

On Euler's problem

Yu. V. Egorov

Institute de Mathématique de Toulouse

Abstract: We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional.
Bibliography: 6 titles.

Keywords: Sturm-Liouville problem, optimization of the first eigenvalue.

DOI: https://doi.org/10.4213/sm8106

Full text: PDF file (500 kB)
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English version:
Sbornik: Mathematics, 2013, 204:4, 539–562

Bibliographic databases:

UDC: 517.972.5
MSC: Primary 74P10; Secondary 34B24, 74G25, 74G30
Received: 23.01.2012 and 17.09.2012

Citation: Yu. V. Egorov, “On Euler's problem”, Mat. Sb., 204:4 (2013), 79–102; Sb. Math., 204:4 (2013), 539–562

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb8106
  • https://doi.org/10.4213/sm8106
  • http://mi.mathnet.ru/eng/msb/v204/i4/p79

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Atanackovic T.M., “The Tallest Column Problem: New First Integrals and Estimates”, C. R. Mec., 347:9 (2019), 626–631  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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