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Impressum

Multiwell rigidity in nonlinear elasticity

Milena Chermisi and Sergio Conti

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\dots\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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Published in: SIAM J. Math. Analysis 42, pp. 1986-2012, 2010.

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