Geodesic
On Euler's problem
Sbornik. Mathematics, Tome 204 (2013) no. 4, pp. 539-562
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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: optimization of the first eigenvalue.
Mots-clés : Sturm-Liouville problem 
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Yu. V. Egorov. On Euler's problem. Sbornik. Mathematics, Tome 204 (2013) no. 4, pp. 539-562. http://geodesic.mathdoc.fr/item/SM_2013_204_4_a3/

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[5] Yu. V. Egorov, “On the Lagrange problem about the strongest column”, C. R. Math. Acad. Sci. Paris, 335:12 (2002), 997–1002 | DOI | MR | Zbl

[6] J. I. Diaz, M. Sauvageot, “Euler's column revisited”, Nonlinear Anal. Real World Appl., 11:4 (2010), 2731–2747 | DOI | MR | Zbl