USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 285-296.

When is the first eigenfunction for the clamped plate equation of fixed sign?

Guido Sweers

It is known that the first eigenfunction of the clamped plate equation,
$\Delta^2 \varphi = \lambda \varphi$ in $\Omega$
$\varphi=\frac{\partial}{\partial n}\varphi=0$ 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.

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Guido Sweers
Applied Mathematical Analysis, ITS Faculty
Delft University of Technology
Mekelweg 4, 2628 CD Delft, The Netherlands

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