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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**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. MR**1328749****[2]**C. Bandle,*Isoperimetric Inequalities and Applications*, Monographs and Studies in Math., No. 7, Pitman, London (1980). MR**572958****[3]**T. Boggio, Sulle funzioni di Green d'ordine*m, Rend. Circ. Mat. Palermo***20**(1905), pp. 97-135.**[4]**G. Buttazzo, M. Giaquinta and S. Hildebrandt,*One-dimensional Variational Problems*, Clarendon Press, Oxford (1998). MR**1694383****[5]**H. C. Grunau and G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions,*Math. Annalen***307**(1997), pp. 589-626. MR**1464133****[6]**B. Kawohl,*Rearrangements and convexity of level sets in P.D.E*., Lecture Notes in Math., No. 1150, Springer, Berlin-New York (1985). MR**810619****[7]**N. S. Nadirashvili, Rayleigh's conjecture on the principal frequency of the clamped plate,*Arch. Ration. Mech. Anal*.**129**(1995), pp. 1-10. MR**1328469****[8]**G. Talenti, Elliptic equations and rearrangements,*Ann. Sc. Norm. Sup. Pisa*, Ser. IV,**3**(1976), pp. 697-718. MR**0601601****[9]**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. MR**0145191**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
35A30,
35B45,
35J40,
74K20

Retrieve articles in all journals with MSC: 35A30, 35B45, 35J40, 74K20

Additional Information

DOI:
https://doi.org/10.1090/qam/1976374

Article copyright:
© Copyright 2003
American Mathematical Society