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arXiv · 2111.15189

Strain Tensors and Matching Property on Surfaces with the Gauss curvature changing sign

Liang-Biao Chen·Peng-Fei Yao
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Abstract

We prove the regularity of solutions to the strain tensor equation on a region $S$ with the Gauss curvature changing sign. Furthermore, we obtain the density property that smooth infinitesimal isometries are dense in the $W^{2,2}(S,\mathbb{R}^3)$ infinitesimal isometries. Finally, the matching property is established. Those results are important tools in obtaining recovery sequences ($\Gamma$-lim sup inequality) for dimensionally-reduced shell theories in elasticity.

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Liang-Biao Chen, Peng-Fei Yao. 2021-11-30. Strain Tensors and Matching Property on Surfaces with the Gauss curvature changing sign. https://arxiv.org/abs/2111.15189

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