A Constructive Proof of Korn’s Scaled Inequalities for Shells

One of Korn's scaled inequalities for shells asserts that the H 1 -norm of a displacement field of a shell with thickness 2ε clamped on a portion of its lateral boundary, once scaled to a domain independent of ε, is bounded above by the L 2 -norm of the corresponding scaled infinitesimal strain tensor field multiplied by a constant of order ε -1 .We give a constructive proof to this inequality, and to other two inequalities of this type, which is thus different from the original proof of Ciarlet et al. [Arch.Rational Mech.Anal.