On a Lagrange problem and its generalizations

V. A. Kondratiev; Yu. V. Egorov

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-12

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Kondratiev, V. A., and Egorov, Yu. V.. "On a Lagrange problem and its generalizations." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-12. <http://eudml.org/doc/112077>.

@article{Kondratiev1993-1994,
author = {Kondratiev, V. A., Egorov, Yu. V.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Sturm-Liouville problem; Lagrange problem; eigenvalue; extremal values},
language = {eng},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On a Lagrange problem and its generalizations},
url = {http://eudml.org/doc/112077},
year = {1993-1994},
}

TY - JOUR
AU - Kondratiev, V. A.
AU - Egorov, Yu. V.
TI - On a Lagrange problem and its generalizations
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - eng
KW - Sturm-Liouville problem; Lagrange problem; eigenvalue; extremal values
UR - http://eudml.org/doc/112077
ER -

References

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  1. [1] J.L. Lagrange, Sur la figure des colonnes. Oeuvres de Lagrange, Paris: Gauthier-Villars, 1867. 
  2. [2] J.B. Keller, The shape of the strongest column, Arch. Rational Mech. Anal., 5, 1960, pp.275-285. MR128160
  3. [3] J.B. Keller, I. Tadjbakhsh, Strongest columns and isoperimetric inequalities for eigenvalues, Journal of Applied Mech.,29, 1962, pp.159-164. Zbl0106.38301MR137381
  4. [4] N. Olhoff, S. Rasmussen, On single and bimodal optimum buckling loads of clamped columns, Ing. Journal Solids Struct., 13, 1977, pp. 605-614. Zbl0357.73041
  5. [5] A.S. Bratus, A.P. Seiranian, Bimodal solutions in eigenvalue optimization problems, Prikl. Mat. Mech. USSR, 47, 1983, pp. 451-457. Zbl0569.47004MR775092
  6. [6] A.P. Seiranian, On a problem of Lagrange, Inzh. Zh., Mehanika Tverdogo Tela, 19, 1984, pp. 101-111. MR776543
  7. [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. Zbl0622.49020MR847441
  8. [8] S.J. Cox, The shape of the ideal column, The Mathematical Intelligencer, 14, 1992, pp. 16-24. Zbl0751.73001MR1147343
  9. [9] S.J. Cox, M.L. Overton, On the optimal design of columns against buckling, SIAM J. Math. Anal., 23, 1992, pp. 287-325. Zbl0793.73070MR1147865
  10. [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. Zbl0553.35063
  11. [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. Zbl0548.34027MR740013
  12. [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. Zbl0721.34017
  13. [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. Zbl0746.34049
  14. [14] V.M. Tikhomirov, V.P. Buslaev, Algebra and Analysis, St.PetersbourgMath. J., 3, n.6 (1992). Zbl0776.34065

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