Positivity for the clamped plate equation under high tension
Abstract
In this article we consider positivity issues for the clamped plate equation with high tension $\gamma>0$. This equation is given by $\Delta^2u  \gamma\Delta u=f$ under clamped boundary conditions. Here we show, that given a positive $f$, i.e. upwards pushing, we find a $\gamma_0>0$ such that for all $\gamma\geq \gamma_0$ the bending $u$ is indeed positive. This $\gamma_0$ only depends on the domain and the ratio of the $L^1$ and $L^\infty$ norm of $f$. In contrast to a recent result by Cassani&Tarsia, our approach is valid in all dimensions.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.09341
 Bibcode:
 2021arXiv210609341E
 Keywords:

 Mathematics  Analysis of PDEs;
 35B09 (Primary) 35B30;
 35B50;
 35J40 (Secondary)
 EPrint:
 Keywords: Bilaplace equation, maximum principle, high tension