The clamped-plate equation for the limaçon

Journal article (2005)

Authors

A Dall'Acqua Analysis - EEMCS
G.H. Sweers Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
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Published Date

2005

Language

Undefined/Unknown

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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