Preprint 98/2002

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

Sergio Conti, Camillo De Lellis, Stefan Müller, and Mario Romeo

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Submission date: 06. Nov. 2002
Pages: 8
published in: Comptes rendus mathematique, 337 (2003) 4, p. 233-238 
DOI number (of the published article): 10.1016/S1631-073X(03)00333-9
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We give a short, self-contained argument showing that, for compact connected sets in formula4 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.

18.10.2019, 02:11