Stationary points of nonlinear plate theories
The author deals with nonlinear plate models expressing for instance thin growing tissues in biology or elastic sheets obtained by controlled polymerization. The reference configuration of the sheet is modelled by a bounded domain \(S\subset \mathbb{R}^2\). The Willmore functional given by \[ W(u)=\frac 14 \int_S H^2\,d\mu_g+\int_{\partial S}\kappa_g\,d\mu_{g\partial} \] plays an important role in his investigations. The relevant case for thin film elasticity is the restriction of the Willmore functional to isometric immersions \[ W_g^{2,2}(S)=\{u\in W^{2,2}(S,\mathbb{R}^3):(\nabla u)^\top (\nabla u)=g\;\text{a.e. in}\;S\}. \]
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