On the ellipticity of linear shell models

We give here a simple proof of the ellipticity of the two-dimensional shell equations proposed by W. T. Koiter. This proof relies on two main tools: a lemma due to J. L. Lions, which he used in a crucial way for establishing Korn's inequality in three dimensional elasticity, and a rigid displacement lemma for shells, due to M. Bernadou and the first author.Dedicated to Professor Klaus Kirchgässner on the occasion of his sixtieth birthdayThis work is part of the Project Junctions in Elastic Multi-Structures of the Program S.C.I.E.N.C.E. of the Commission of the European Communities (contract No. SC1*0473-C(EDB)).