On the Positivity Preserving Property of Hinged Plates
Enea Parini, Athanasios Stylianou · SIAM Journal on Mathematical Analysis · 2009
In this work we show that the Kirchhoff–Love model for a hinged plate $\Delta^2 v = f \text{ in }E,\; v = \Delta v - (1 - \sigma) \kappa v_n = 0 \text{ on }\partial E$ admits, for $f \in L^2(E)$ and $-1 < \sigma < 1$, a unique weak solution in $W^{2,2}(E) \cap W^{1,2}_0(E)$ which satisfies the positivity preserving property when $E \subset \mathbb{R}^2$ is a bounded, convex domain with $\mathcal{C}^{2,1}$ boundary.