Rearrangements and fourth order equations
Authors:
Vincenzo Ferone and Bernd Kawohl
Journal:
Quart. Appl. Math. 61 (2003), 337-343
MSC:
Primary 35A30; Secondary 35B45, 35J40, 74K20
DOI:
https://doi.org/10.1090/qam/1976374
MathSciNet review:
MR1976374
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Abstract: The paper contains a priori estimates for the deformation of plates and beams. In particular we investigate the “worst cases” for the maximum deformation depending on where a load is placed on a beam or plate. The methods of proof use rearrangement argument.
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M. S. Ashbaugh and R. D. Benguria, On Rayleigh’s conjecture for the clamped plate and its generalization to three dimensions, Duke Math. J. 78 (1995) pp. 1–17.
C. Bandle, Isoperimetric Inequalities and Applications, Monographs and Studies in Math., No. 7, Pitman, London (1980).
T. Boggio, Sulle funzioni di Green d’ordine m, Rend. Circ. Mat. Palermo 20 (1905), pp. 97–135.
G. Buttazzo, M. Giaquinta and S. Hildebrandt, One-dimensional Variational Problems, Clarendon Press, Oxford (1998).
H. C. Grunau and G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Annalen 307 (1997), pp. 589–626.
B. Kawohl, Rearrangements and convexity of level sets in P.D.E., Lecture Notes in Math., No. 1150, Springer, Berlin-New York (1985).
N. S. Nadirashvili, Rayleigh’s conjecture on the principal frequency of the clamped plate, Arch. Ration. Mech. Anal. 129 (1995), pp. 1–10.
G. Talenti, Elliptic equations and rearrangements, Ann. Sc. Norm. Sup. Pisa, Ser. IV, 3 (1976), pp. 697–718.
H. P. Weinberger, Symmetrization in uniformly elliptic problems, in: Studies in Math Analysis and Related Topics, Univ. of Calif. Press, Stanford, CA (1962), pp. 424–428.
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© Copyright 2003
American Mathematical Society
