The clamped-plate equation for the limaçon
Journal Article
(2005)
Research Group
Analysis
DOI related publication
https://doi.org/doi:10.1007/s10231-004-0121-9
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https://resolver.tudelft.nl/uuid:cde1bbd5-3e61-4938-a874-611a5cb2881a
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Publication Year
2005
Research Group
Analysis
Bibliographical Note
in 2004 electronische versie opgevoerd, sb@en
Issue number
3
Volume number
184
Pages (from-to)
361-374
Abstract
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
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