The asymptotically sharp Korn interpolation and second inequalities for shells
Davit Harutyunyan · Comptes Rendus Mathématique · 2018
We consider shells in three-dimensional Euclidean space that have bounded principal curvatures. We prove Korn's interpolation (or the so-called first and a half 1 ) and the second inequalities on that kind of shells for u ∈ W 1 , 2 vector fields, imposing no boundary or normalization conditions on u . The constants in the estimates are optimal in terms of the asymptotics in the shell thickness h , having the scalings h or O ( 1 ) . The Korn interpolation inequality reduces the problem of deriving any linear Korn type estimate for shells to simply proving a Poincaré-type estimate with the symmetrized gradient on the right-hand side. In particular, this applies to linear geometric rigidity estimates for shells, i.e. Korn's fist inequality without boundary conditions.