SEMINAR @ SISSA, Prof. M. Lewicka - Wed 14 Jan at 14.00 hrs.

[Barbara Corzani]

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FUNCTIONAL ANALYSIS SECTOR'S ACTIVITIES
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SEMINAR

Prof. Marta Lewicka
(University of Minnesota)

Title: The matching property of infinitesimal isometries on elliptic 
surfaces and elasticity of thin shells

Wed 14 Jan 2009  @  2:00 pm

SISSA - Main Building - ground floor - room B

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Abstract: A longstanding problem in the mathematical theory of elasticity 
is to predict theories of lower-dimensional objects (such as rods, plates 
or shells), subject to mechanical deformations, starting from the 3d 
nonlinear theory. For plates, a recent effort has lead to rigorous 
justification of a hierarchy of such theories (membrane, Kirchhoff, von 
Karman). For shells, despite extensive use of their ad-hoc generalizations 
present in the engineering applications, much less is known from the 
mathematical point of view.

In this talk, I will discuss the limiting behavior (using the notion of 
Gamma-limit) of the 3d nonlinear elasticity for thin elliptic shells,
as their thickness h converges to 0, under the assumption that the elastic 
energy of deformations scales like h^\beta, with 2<\beta<4.

Two major ingredients of the proofs are: the density of smooth isometries 
of Sobolev first order isometries, and a result on matching smooth 
infinitesimal isometries with exact isometric immersions on smooth 
elliptic surfaces.