Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells

Abstract

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain $L^2$ regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the $L^2$ regularity for non-characteristic regions. Finally, we obtain the optimal constant in the first Korn inequality scales like $h^{4/3}$ for hyperbolic shells, generalizing the assumption that the middle surface of the shell is given by a single principal system in the literature.

arXiv comment39 pages. arXiv admin note: text overlap with arXiv:1708.07202

References in corpus (4)

• Space of Infinitesimal Isometries and Bending of Shells
• Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shells
• On the Korn interpolation and second inequalities in thin domains
• Linear Strain Tensors on Hyperbolic Surfaces and Asymptotic Theories for Thin Shells

Cited by in corpus (4)

• Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shells
• Linear Strain Tensors on Hyperbolic Surfaces and Asymptotic Theories for Thin Shells
• The linearized Kirchhoff theory for plates with incompatible prestrain
• Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells