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Sbornik: Mathematics, 2013, Volume 204, Issue 4, Pages 539–562
DOI: https://doi.org/10.1070/SM2013v204n04ABEH004311 (Mi sm8106) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Euler's problem

Yu. V. Egorov

Institute de Mathématique de Toulouse
English version PDF (311 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2013v204n04ABEH004311
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.
Received: 23.01.2012 and 17.09.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 4, Pages 79–102
DOI: https://doi.org/10.4213/sm8106
Bibliographic databases:
Document Type: Article
UDC: 517.972.5
MSC: Primary 74P10; Secondary 34B24, 74G25, 74G30
Language: English
Original paper language: Russian
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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  • https://doi.org/10.1070/SM2013v204n04ABEH004311
  • https://www.mathnet.ru/eng/sm/v204/i4/p79
    • This publication is cited in the following 1 articles:
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    Russian version PDF:224
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    References:59
    First page:61
     
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