Calculus of Variations and Geometric Measure Theory

M. Chermisi - S. Conti

Multiwell rigidity in nonlinear elasticity

created by chermisi on 17 Sep 2008
modified on 19 Feb 2011


Published Paper

Inserted: 17 sep 2008
Last Updated: 19 feb 2011

Journal: SIAM J. Math. Anal.
Year: 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.