#### Vol. 11, No. 5, 2018

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The shape of low energy configurations of a thin elastic sheet with a single disclination

### Heiner Olbermann

Vol. 11 (2018), No. 5, 1285–1302
##### Abstract

We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved energy scaling law, removing the next-to-leading-order terms in the lower bound. Then we prove the convergence of (almost-)minimizers of the free elastic energy towards the shape of a radially symmetric cone, up to Euclidean motions, weakly in the spaces ${W}^{2,2}\left({B}_{1}\setminus {B}_{\rho };{ℝ}^{3}\right)$ for every $0<\rho <1$, as the thickness $h$ is sent to 0.

##### Keywords
nonlinear elasticity, thin elastic sheets, d-cones, Hessian determinant
##### Mathematical Subject Classification 2010
Primary: 49Q10, 74K20
##### Milestones
Received: 20 July 2017
Revised: 9 October 2017
Accepted: 22 November 2017
Published: 11 April 2018
##### Authors
 Heiner Olbermann Universität Leipzig Leipzig Germany