### Abstract

We consider the following question: given a set of matrices Jf with no rank-one connections, does it support a nontrivial Young measure limit of gradients? Our main results are these: (a) a Young measure can be supported on four incompatible matrices; (b) in two space dimensions, a Young measure cannot be supported on finitely many incompatible elastic wells; (c) in three or more space dimensions, a Young measure can be supported on three incompatible elastic wells; and (d) if k supports a nontrivial Young measure with mean value 0, then the linear span of Jf must contain a matrix of rank one.

Original language | English (US) |
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Pages (from-to) | 843-878 |

Number of pages | 36 |

Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |

Volume | 124 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1994 |

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## Cite this

Bhattacharya, K., Firoozye, N. B., James, R. D., & Kohn, R. V. (1994). Restrictions on microstructure.

*Proceedings of the Royal Society of Edinburgh: Section A Mathematics*,*124*(5), 843-878. https://doi.org/10.1017/S0308210500022381