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 language | Undefined/Unknown |
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Pages (from-to) | 1-14 |
Number of pages | 14 |
Journal | Annali di Matematica Pura ed Applicata |
Publication status | Published - 2004 |
Keywords
- Vakpubl., Overig wet. > 3 pag