The Matching Property of Infinitesimal Isometries on Elliptic Surfaces
and Elasticity of Thin Shells
Marta Lewicka
University of Minnesota
Department of Mathematics
127 Vincent Hall
206 Church St. S.E.
Minneapolis, MN 55455, USA
email lewicka@math.umn.edu
Maria Giovanna Mora
Scuola Internazionale Superiore di Studi Avanzati
via Beirut 2-4
34014 Trieste, Italy
email mora@sissa.it
Mohammad Reza Pakzad
University of Pittsburgh
Department of Mathematics
139 University Place
Pittsburgh, PA 15260
email pakzad@pitt.edu
Abstract: Using the notion of 
-convergence, we discuss the limiting behavior of
the 3d nonlinear elastic energy for thin elliptic shells, as their thickness
converges to zero, under the assumption that the elastic energy of
deformations scales like 
with 
. 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 
first order infinitesimal isometries, and a result
on matching smooth infinitesimal isometries with exact isometric immersions on
smooth elliptic surfaces.
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