Title Polyconvexity equals rank-one convexity for connected isotropic sets in $\Bbb M^{2\times 2}$. Publication Type Journal Article Year of Publication 2003 Authors Conti S., De Lellis C., Müller S., Romeo M. Journal Comptes Rendus Mathématique. Académie des Sciences. Paris Volume 337 Pagination 233–238 Publisher Elsevier Type of Article calculus of variations ISSN 1631-073X Keywords integral functionals, quasiconvexity, singular values Abstract We give a short, self-contained argument showing that, for compact connected sets in M2x2 which are invariant under the left and right action of SO(2), polyconvexity is equivalent to rank-one convexity (and even to lamination convexity). As a corollary, the same holds for O(2)-invariant compact sets. These results were first proved by Cardaliaguet and Tahraoui. We also give an example showing that the assumption of connectedness is necessary in the SO(2) case. Notes C. R. Math. Acad. Sci. Paris 337 (2003), no. 4, 233–238. URL https://www.sciencedirect.com/science/article/pii/S1631073X03003339 DOI 10.1016/S1631-073X(03)00333-9
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