ELLIPTICITY OF THE MEMBRANE EQUATIONS OF A UNIFORMLY ELLIPTIC SHELL

We give a new proof of the existence and uniqueness of the solution of the two-dimensional membrane equations of a linearly elastic shell wh ose middle surface is uniformly elliptic. The existence proof relies i n particular on a lemma that J.-L. Lions has established for proving t he three-dimensional Korn inequality. The uniqueness proof uses the un iqueness of the Cauchy problem due to A. Calderon, then the uniqueness of the extension of the solution of some elliptic equations due to N. Aronszajn.