Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 267-283.
Title: When is the first eigenfunction for the clamped plate equation of fixed sign?
Author: Guido Sweers (Delft Univ. of Technology, The Netherlands)
Abstract:
It is known that the first eigenfunction of the clamped plate equation,
$\Delta^2 \varphi = \lambda \varphi$ in $\Omega$
with
$\varphi=\frac{\partial}{\partial n}\varphi=0$ on $\partial\Omega$,
is not necessarily of fixed sign.
In this article, we survey the relations between domains
$\Omega$ and the sign of that first eigenfunction.
Published January 8, 2001.
Math Subject Classifications: 35J30, 35P99.
Key Words: Clamped plate; first eigenfunction; maximum principle; biharmonic.