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.
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Mathematics Subject Classification (2000)
35J40, 35Q72, 35B50
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Dall’Acqua, A., Sweers, G. The clamped-plate equation for the limaçon. Annali di Matematica 184, 361–374 (2005). https://doi.org/10.1007/s10231-004-0121-9
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DOI: https://doi.org/10.1007/s10231-004-0121-9