# Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2

Conti, S; De Lellis, C; Müller, S; Romeo, M (2003). Polyconvexity equals rank-one convexity for connected isotropic sets in M2×2. Comptes Rendus Mathématique. Académie des Sciences. Paris, 337(4):233-238.

## 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.

## 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.

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