Abstract
AbstractIn this article, we consider positivity issues for the clamped plate equation with high tension $$\gamma >0$$
γ
>
0
. This equation is given by $$\Delta ^2u - \gamma \Delta u=f$$
Δ
2
u
-
γ
Δ
u
=
f
under clamped boundary conditions. Here, we show that given a positive f, i.e. upwards pushing, we find a $$\gamma _0>0$$
γ
0
>
0
such that for all $$\gamma \ge \gamma _0$$
γ
≥
γ
0
the bending u is indeed positive. This $$\gamma _0$$
γ
0
only depends on the domain and the ratio of the $$L^1$$
L
1
and $$L^\infty $$
L
∞
norm of f. In contrast to a recent result by Cassani and Tarsia, our approach is valid in all dimensions.
Funder
Eberhard Karls Universität Tübingen
Publisher
Springer Science and Business Media LLC
Cited by
1 articles.
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