\(T_5\)-configurations and non-rigid sets of matrices (Q1703145)

Based on the notion of \(T_{N}\)-configuration (already used for \(N=4\) in the context of differential inclusions by \textit{S. Müller} and \textit{V. Šverák} [Ann. Math. (2) 157, No. 3, 715--742 (2003; Zbl 1083.35032)]), the authors introduce the notion of large \(T_{5}\)-set. The main result in the paper states that if a \(5\) element set \(K\) of \(2\times 2\) matrices is a large \(T_{5}\)-set, then it is non-rigid, that is, the differential inclusion \(Du(x)\in K,\) \(x\in \Omega \) (with \(\Omega \) being a bounded domain with Lipschitz boundary) admits non-affine Lipschitz solutions.