A clamped plate with a uniform weight may change sign

Hans-Christoph Grunau; Guido Sweers

doi:10.3934/dcdss.2014.7.761

Article Contents

2014, Volume 7, Issue 4: 761-766. Doi: 10.3934/dcdss.2014.7.761

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A clamped plate with a uniform weight may change sign

Hans-Christoph Grunau^1, and
Guido Sweers^2,

1.
Fakultät für Mathematik, Otto-von-Guericke Universität, Postfach 4120, 39016 Magdeburg
2.
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln

Received: June 30, 2013

Revised: August 31, 2013

Published: July 2014

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Abstract

It is known that the Dirichlet bilaplace boundary value problem, which is used as a model for a clamped plate, is not sign preserving on general domains. It is also known that the corresponding first eigenfunction may change sign. In this note we will show that even a constant right hand side may result in a sign-changing solution.

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Mathematics Subject Classification: Primary: 35J40; Secondary: 35B50.

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