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 ⊂Rn and for ε small, there exist nonconstant localminimisers uε satisfying uε≃±1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit uε→u() the hypersurface separating the states u0= 1 and u0=-1 locally minimises surface area. Generalisations are discussed with, for example, vector-valued u and anisotropic perturbations replacing’∇u’2.
|Original language||English (US)|
|Number of pages||16|
|Journal||Proceedings of the Royal Society of Edinburgh: Section A Mathematics|
|State||Published - Jan 1 1989|
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