Strain Tensors and Matching Property on Degenerated Hyperbolic Surfaces

2021/07/20 by Chen, Liang-Biao, Yao, Peng-Fei
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.09269

Abstract

We prove the regularity of solutions to the strain tensor equation on degenerated hyperbolic surfaces S where the Gauss curvature is zero on a part of boundary. Furthermore, we obtain the density property that smooth infinitesimal isometries are dense in the W^2,2(S,\R³) infinitesimal isometries. Finally, the matching property is established. Those results are important tools in obtaining recovery sequences (\Ga-lim sup inequality) for dimensionally-reduced shell theories in elasticity.

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