  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.
