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MiS 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

Abstract

We give a short, self-contained argument showing that, for compact connected sets in M2×2 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.

Contact the author per mail Download full preprint 171 KB
Received:
06.11.02
Published:
06.11.02

Related publications

inJournal
2003 Repository Open Access
Sergio Conti, Camillo De Lellis, Stefan Müller and Mario Romeo

Polyconvexity equals rank-one convexity for connected isotropic sets in M 2*2

In: Comptes rendus mathematique, 337 (2003) 4, pp. 233-238
BibTex DOI: 10.1016/S1631-073X(03)00333-9