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MiS Preprint
47/2001
Quasiconvex hulls in symmetric matrices
Georg Dolzmann
Abstract
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 $ac - b^2 \geq 0$ 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.
