### Abstract

We construct local minimisers to certain variational problems. The method is quite general and relies on the theory of F-convergence. The approach is demonstrated through the model problem [formula ommittes] It is shown that in certain nonconvex domains The approach is demonstrated through the model problem Ω ⊂R^{n} and for ε small, there exist nonconstant localminimisers u^{ε} satisfying u^{ε≃±}1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit u^{ε→}u^{()} the hypersurface separating the states u_{0}= 1 and u_{0}=-1 locally minimises surface area. Generalisations are discussed with, for example, vector-valued u and anisotropic perturbations replacing’∇_{u}’^{2}.

Original language | English (US) |
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Pages (from-to) | 69-84 |

Number of pages | 16 |

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

Volume | 111 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1 1989 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Royal Society of Edinburgh: Section A Mathematics*,

*111*(1-2), 69-84. https://doi.org/10.1017/S0308210500025026