The clamped-plate equation for the limaçon

A Dall'Acqua, GH Sweers

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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. Keywords clamped plate - biharmonic - positivity - nonconvex Mathematics Subject Classification (2000) 35J40, 35Q72, 35B50
Original languageUndefined/Unknown
Pages (from-to)361-374
Number of pages14
JournalAnnali di Matematica Pura ed Applicata
Issue number3
Publication statusPublished - 2005


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