

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
Bibtex
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Abstract:
We give a short, self-contained argument showing that, for compact connected sets in
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.