2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174157Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like $h^β$ with $2<β<4$. We establish that, for the given scaling regime, the limiting theory reduces to the linear pure bending. Two major ingredients of the proofs are: the density of smooth infinitesimal isometries in the space of $W^{2,2}$ first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.21 pagesAnalysis of PDEs74K20; 74B20text