Multiwell Rigidity in Nonlinear Elasticity
Milena Chermisi, Sergio Conti · SIAM Journal on Mathematical Analysis · 2010
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.