AN EXISTENCE AND UNIQUENESS THEOREM FOR THE 2-DIMENSIONAL LINEAR MEMBRANE SHELL EQUATIONS

We consider the two-dimensional membrane equations of a linearly elast ic clamped shell, whose middle surface is uniformly elliptic. The elim ination of the normal component of the displacement yields a reduced v ariational problem whose strain energy vanishes for some non-zero tens ors. The application of the theory of S. Agmon, A. Douglis and L. Nire nberg to an auxiliary uniformly elliptic first-order system neverthele ss allows to show that the bilinear form of the reduced problem is H-0 (1)-elliptic.