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Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells
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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.
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Cited by 1 Pith paper
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Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells
The optimal thickness exponent in the nonlinear geometric rigidity inequality is at least 4/3 (hyperbolic), 1 (elliptic), and 3/2 (parabolic) shells.
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