Stationary points of nonlinear plate theories
type: Item
instance of: scholarly article
title: Stationary points of nonlinear plate theories
zbMATH Open document ID: 1368.74014
author: Peter Hornung
published in: Journal of Functional Analysis
publication date: 2017-06-19T00:00:00Z
review text: 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 \[ W_g^{2,2}(S)=\{u\in W^{2,2}(S,\mathbb{R}^3):(\nabla u)^\top (\nabla u)=g\;\text{a.e. in}\;S\}. \]
reviewed by: Igor Bock
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74G55
zbMATH DE Number: 6732242
zbMATH Keywords: non-Euclidean plates
zbMATH Keywords: Willmore functional
zbMATH Keywords: infinitesimal bendings
MaRDI profile type: Publication
full work available at URL: j.jfa.2017.04.010
OpenAlex ID: W2609962039
Wikidata QID: Q125378788
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DOI: 10.1016/J.JFA.2017.04.010
description: scientific article