17:00
Recently Friesecke, James and Muller established the following
quantitative version of the rigidity of SO(n) the group of special orthogonal
matrices. Let U be a bounded Lipschitz domain. Then there exists a constant
C(U) such that for any mapping v in the L2-Sobelev space the L^2-distance of
the gradient controlls the distance of v a a single roation.
This interesting inequality is fundamental in several problems concerning
dimension reduction in nonlinear elasticity.
In this talk, we will present a joint work with Muller and Zhong where we
investigate an analagous quantitative estimate where we replace SO(n) by an
arbitrary smooth, compact and SO(n) invariant subset of the conformal
matrices E. The main novelty is that exact solutions to the differential
inclusion Df(x) in E a.e.x in U are not necessarily affine mappings.