Annali di Matematica Pura ed Applicata

, Volume 184, Issue 3, pp 361–374

The clamped-plate equation for the limaçon


DOI: 10.1007/s10231-004-0121-9

Cite this article as:
Dall’Acqua, A. & Sweers, G. Annali di Matematica (2005) 184: 361. doi:10.1007/s10231-004-0121-9


Hadamard claimed in 1907 that the clamped-plate equation is positivity preserving for domains which are bounded by a Limaçon de Pascal. We will show that this claim is false in its full generality. However, we will also prove that there are nonconvex limaçons for which the clamped-plate equation has the sign-preserving property. In fact we will give an explicit bound for the parameter of the limaçon where sign change may occur.


clamped platebiharmonicpositivitynonconvex

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Applied Mathematical Analysis, ITS FacultyDelft University of TechnologyDelftThe Netherlands