, Volume 184, Issue 3, pp 361-374
Date: 15 Oct 2004

The clamped-plate equation for the limaçon

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Abstract

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.

Mathematics Subject Classification (2000)

35J40, 35Q72, 35B50