Multiwell rigidity in nonlinear elasticity
Abstract
We derive a quantitative rigidity estimate for a multiwell problem in nonlinear elasticity. Precisely, we show that if a gradient field is L1-close to a set of the form SO(n)U1 ... SO(n)Ul, 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)Ui. The estimate holds for any connected subdomain, and has the optimal scaling.
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