Multiwell rigidity in nonlinear elasticity

Details Multiwell rigidity in nonlinear elasticity Multiwell rigidity in nonlinear elasticity

2008-02-07

arxiv.org/abs/0802.0955v1

Mathematics

Analysis of PDEs

23 pages, 3 figures

Scientific paper

We derive a quantitative rigidity estimate for a multiwell problem in nonlinear elasticity. Precisely, we show that if a gradient field is L^1-close to a set of the form SO(n)U_1 \cup ... \cup SO(n)U_l, and an appropriate bound on the length of the interfaces holds, then the gradient field is actually close to only one of the wells SO(n)U_i. The estimate holds for any connected subdomain, and has the optimal scaling.

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