  We consider singular perturbations of elliptic systems depending on a
parameter ? such that, for ? = 0 the boundary conditions are not adapted to the
equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit
holds only in very abstract spaces out of distribu- tion theory involving
complexi?cation and non-local phenomena. This system appears in the thin shell
theory when the middle surface is el- liptic and the shell is fixed on a part
of the boundary and free on the rest. We use a heuristic reasoning applying
some simplifications which allow to reduce the original problem in a domain to
another problem on its boundary. The novelty of this work is that we consider
systems of partial differential equations while in our previous work we were
dealing with single equations.
