On internal and boundary layers with unbounded energy in thin shell theory. Elliptic case

Abstract

We consider the system of equations of Koiter thin shell theory in a slightly simplified form, in the case when the limit (for small thickness) problem is elliptic, i.e., the principal curvatures of the middle surface are everywhere of the same sign. Under singular loadings, which are not in the dual of the energy space of the limit problem, the energy of the solutions grows without limit as the thickness tends to zero. Moreover, it concentrates on boundary layers along the singularities of the loading. We define and prove the convergence to the leading order term in that layers.