On a Lagrange problem and its generalizations
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1993-1994), Exposé no. 13, 12 p.
@article{SEDP_1993-1994____A14_0,
     author = {Kondratiev, V. A. and Egorov, Yu. V.},
     title = {On a {Lagrange} problem and its generalizations},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:13},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1993-1994},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_1993-1994____A14_0/}
}
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Kondratiev, V. A.; Egorov, Yu. V. On a Lagrange problem and its generalizations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1993-1994), Exposé no. 13, 12 p. http://www.numdam.org/item/SEDP_1993-1994____A14_0/

[1] J.L. Lagrange, Sur la figure des colonnes. Oeuvres de Lagrange, Paris: Gauthier-Villars, 1867.

[2] J.B. Keller, The shape of the strongest column, Arch. Rational Mech. Anal., 5, 1960, pp.275-285. | MR 128160

[3] J.B. Keller, I. Tadjbakhsh, Strongest columns and isoperimetric inequalities for eigenvalues, Journal of Applied Mech.,29, 1962, pp.159-164. | MR 137381 | Zbl 0106.38301

[4] N. Olhoff, S. Rasmussen, On single and bimodal optimum buckling loads of clamped columns, Ing. Journal Solids Struct., 13, 1977, pp. 605-614. | Zbl 0357.73041

[5] A.S. Bratus, A.P. Seiranian, Bimodal solutions in eigenvalue optimization problems, Prikl. Mat. Mech. USSR, 47, 1983, pp. 451-457. | MR 775092 | Zbl 0569.47004

[6] A.P. Seiranian, On a problem of Lagrange, Inzh. Zh., Mehanika Tverdogo Tela, 19, 1984, pp. 101-111. | MR 776543

[7] A.S. Bratus, Multiple eigenvalues in problems of optimizing, The spectral properties of systems with a finite number of degrees of freedom. USSR Compt. Math. and Math. Phys., 26, 1986, pp.1-7. | MR 847441 | Zbl 0622.49020

[8] S.J. Cox, The shape of the ideal column, The Mathematical Intelligencer, 14, 1992, pp. 16-24. | MR 1147343 | Zbl 0751.73001

[9] S.J. Cox, M.L. Overton, On the optimal design of columns against buckling, SIAM J. Math. Anal., 23, 1992, pp. 287-325. | MR 1147865 | Zbl 0793.73070

[10] Yu.V. Egorov, V.A. Kondratiev, On an estimate of the first eigen-value for a self-adjoint elliptic operator, Vestnik Mosk. un-ta, Mathem., Mechanics, 3, 1983, pp. 46-52. | Zbl 0553.35063

[11] Yu.V. Egorov, V.A. Kondratiev, On estimates of the first eigen-value of the Sturm-Liouville problem, Russian Math. Surveys, 39 (2), 1984, pp. 151-152. | MR 740013 | Zbl 0548.34027

[12] Yu.V. Egorov, V.A. Kondratiev, On an estimate for the first eigen-value of the Sturm-Liouville operator, Vestnik Mosk. un-ta, Mathem., Mechanics, 6, 1990, pp. 75-78. | Zbl 0721.34017

[13] Yu. V. Egorov, V.A. Kondratiev, On an estimate for the principal eigenvalue of the Sturm-Liouville operator, Vestnik Mosk. un-ta, Mathem., Mechanics, 6, 1991, pp. 5-11. | Zbl 0746.34049

[14] V.M. Tikhomirov, V.P. Buslaev, Algebra and Analysis, St.Petersbourg Math. J., 3, n.6 (1992).