On the isoperimetric inequality for the buckling of a clamped plate

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 54, Issue 5, 2003, Pages 756-770

  Ashbaugh, Mark S ^a   Bucur, Dorin ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Buckling load; Clamped plate; Isoperimetric inequality

Indexed keywords

EID: 0141457340     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-3204-3     Document Type: Article

References (21)

1. Ashbaugh, M. S.; Benguria, R. D., Proof of the Payne-Pólya-Weinberger conjecture, Bull. Amer. Math. Soc. 25 (1991), 19-29.
2. Bucur, D.; Varchon, N., Global minimizer of the first eigenvalue of an elliptic operator with non-constant coefficients, Electron. J. Differential Equations 36 (2000), 1-10, http:/ejde.math.swt.edu.
3. Bucur D.; Zolésio, J. P., N-dimensional shape optimization under capacitary constraints, J. Diff. Eq. 123 (1995), 504-522.
4. Buttazzo, G.; Dal Maso, G., Shape optimization for Dirichlet problems: relaxed formulation and optimally conditions, Appl. Math. Optim. 23 (1991), 17-49.
5. Buttazzo, G.; Dal Maso, G., An existence result for a class of shape optimization problems, Arch. Rational Mech. Anal. 122 (1993), 183-195.
6. Esteban M. J.; Lions, P. L., F-convergence and the concentration-compactness method for some variational problems with lack of compactness, Ricerche di Matematica XXXVI, fasc. 1 (1987), 73-101.
7. Hedberg, L. I., Spectral synthesis in Sobolev spaces, and uniqueness of solutions of the Dirichlet problem, Acta Math. 147 (1981), 237-264.
8. Heinonen, J.; Kilpelainen, T.; Martio O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, 1993.
9. Kavian, O., Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Mathématiques et applications 13, Springer-Verlag, 1993.
10. Kawohl B., Some nonconvex shape optimization problems, in Optimal Shape Design, A. Cellina, A. Ornelas, editors, Lect. Notes in Math. 1740, Springer, 2000, pp. 7-46 (see especially Sect IV, pp. 37-44).
11. Kilpelainen, T.; Maly J., Supersolutions to degenerate elliptic equations on quasi-open sets, Commun, in Partial Diff. Eqs. 17 (1992), 371-405.
12. Lieb, E., On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. Math. 74 (1983), 441-448.
13. Lions, P. L., The concentration-compactness principle in the calculus of variations. The locally compact case, part 1, Ann. Inst. Poincaré 1 (1984), 109-145.
14. Payne, L. B., Inequalities for eigenvalues of membranes and plates, J. Rational Mech. Anal. 4 (1955), 517-529.
15. Payne, L. B., Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453-488.
16. Payne, L. E.; Pólya, G.; Weinberger, H. F., Sur le quotient de deux fréquences propres consécutives, C. R. Acad. Sci. Paris 241 (1955), 917-919.
17. Payne, L. E.; Pólya, G.; Weinberger, H. F., On the ratio of consecutive eigenvalues, J. Math. and Phys. 35 (1956), 289-298.
18. Sverak, V., On optimal shape design, J. Math. Pures Appl. 72 (1993), 537-551.
19. Sokolowski, J.; Zolésio, J. P., Introduction to Shape Optimization, Shape Sensitivity Analysis. Springer Series in Computational Mathematics, 16. Springer-Verlag, Berlin, 1992.
20. Willem, M., Analyse harmonique réele, Hermann, Paris, 1995.
21. Willms, B., An isoperimetric inequality for the buckling of a clamped plate, Lecture at the Oberwolfach meeting on "Qualitative properties of PDE" (organized by H. Berestycki, B. Kawohl, and G. Talenti), Feb. 1995.