Calculus of Variations and Geometric Measure Theory
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H. Olbermann

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

created by olbermann on 23 Jul 2019

[BibTeX]

preprint

Inserted: 23 jul 2019

Year: 2017

ArXiv: 1702.06468 PDF

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 $W^{2,2}(B_1\setminus B_\rho;\mathbb{R}^3)$ for every $0<\rho<1$, as the thickness $h$ is sent to 0.

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