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A clamped plate with a uniform weight may change sign

by Hans-Christoph Grunau, Guido Sweers.

Series: 2013-10, Preprints

35J40 Boundary value problems for higher-order elliptic equations
35B50 Maximum principles

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.

clamped plate equation, uniform load, sign changing solution