MiS Preprint Repository

We analyze the semiconvex hulls of the subset K in symmetric matrices given by $K=\{F\in {\mathbb{M}}^{2\times 2}:F^T=F,|F_{11}|=\alpha ,|F_{12}|=b,|F_{22}|=c\}$ that was first considered by Dacorogna & Tanteri [Commun. in PDEs 2001]. We obtain explicit formulae for the polyconvex, the quasiconvex, and the rank-one convex hull for $ac-b^2\ge 0$ and show in particular that the quasiconvex and the polyconvex hull are different if strict inequality holds. For $ac-b^2<0$ we obtain a closed form for the polyconvex and the rank-one convex hull.