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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