### Abstract

This paper studies a vectorial problem in the calculus of variations arising in the theory of martensitic microstructure. The functional has an integral representation where the integrand is a non-convex function of the gradient with exactly four minima. We prove that the Young measure corresponding to a minimizing sequence is homogeneous and unique for certain linear boundary conditions. We also consider the singular perturbation of the problem by higher-order gradients. We study an example of microstructure involving infinite sequential lamination and calculate its energy and length scales in the zero limit of the perturbation.

Original language | English |
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Pages (from-to) | 185-207 |

Number of pages | 23 |

Journal | European Journal of Applied Mathematics |

Volume | 8 |

Issue number | 2 |

Publication status | Published - Apr 1997 |

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## Cite this

Winter, M. (1997). An example of microstructure with multiple scales.

*European Journal of Applied Mathematics*,*8*(2), 185-207.